Relevant bibliographies by topics / Set Theory

Academic literature on the topic 'Set Theory'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 August 2024

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Journal articles on the topic "Set Theory"

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Farah, Ilijas, Sy-David Friedman, Menachem Magidor, and W. Hugh Woodin. "Set Theory." Oberwolfach Reports 11, no. 1 (2014): 91–144. http://dx.doi.org/10.4171/owr/2014/02.

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Farah, Ilijas, Sy-David Friedman, Ralf-Dieter Schindler, and W. Hugh Woodin. "Set Theory." Oberwolfach Reports 14, no. 1 (January 2, 2018): 527–89. http://dx.doi.org/10.4171/owr/2017/11.

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Farah, Ilijas, Ralf-Dieter Schindler, Dima Sinapova, and W. Hugh Woodin. "Set Theory." Oberwolfach Reports 17, no. 2 (July 1, 2021): 797–855. http://dx.doi.org/10.4171/owr/2020/14.

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Neidhöfer, Christoph. "Set Theory." Zeitschrift der Gesellschaft für Musiktheorie [Journal of the German-Speaking Society of Music Theory] 1–2, no. 2/2–3 (2005): 219–27. http://dx.doi.org/10.31751/530.

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Merrell, Patrick. "Set Theory." Scientific American 295, no. 6 (December 2006): 110. http://dx.doi.org/10.1038/scientificamerican1206-110.

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Farah, Ilijas, Ralf Schindler, Dima Sinapova, and W. Hugh Woodin. "Set Theory." Oberwolfach Reports 19, no. 1 (March 10, 2023): 79–106. http://dx.doi.org/10.4171/owr/2022/2.

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Hajek, P., and Z. Hanikova. "Interpreting lattice-valued set theory in fuzzy set theory." Logic Journal of IGPL 21, no. 1 (July 18, 2012): 77–90. http://dx.doi.org/10.1093/jigpal/jzs023.

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Jiang, Jingying. "From Set Theory to the Axiomatization of Set Theory." Highlights in Science, Engineering and Technology 88 (March 29, 2024): 243–47. http://dx.doi.org/10.54097/nbmg4652.

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Axiomatic set theory was created by German mathematician Zermelo as a strategy for addressing and resolving paradoxes in the field of mathematical study. By adopting this strategy, the axiomatic technique will be applied to set theory. The person argues that Cantor's failure to impose restrictions on the idea of a set is the cause of the dilemma. They also claim that Cantor's definition of a set is unclear. Both of these arguments are predicated on the idea that Cantor neglected to place limitations on the idea of a set. Zermelo hypothesized that the condensed version of the axioms would make it easier to define a set and elaborate on its properties, and he was correct in his prediction. The creation of an axiomatization for set theory is the first of this research's main goals. Second, the investigation of various set theory development methods in comparison to one another. Even though there are intriguing puzzles in the field of set theory that have not yet been solved, the axiomatization of set theory is widely regarded as a significant accomplishment in the field.
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Takeuti, Gaisi. "Proof theory and set theory." Synthese 62, no. 2 (February 1985): 255–63. http://dx.doi.org/10.1007/bf00486049.

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Slater, Hartley. "Aggregate Theory Versus Set Theory." Philosophia Scientae, no. 9-2 (November 1, 2005): 131–44. http://dx.doi.org/10.4000/philosophiascientiae.530.

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Dissertations / Theses on the topic "Set Theory"

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Dieterly, Andrea K. "Set Theory." Bowling Green State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1304689030.

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Corella, Francisco. "Mechanizing set theory." Thesis, University of Cambridge, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.334076.

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Atmai, Rachid. "Contributions to Descriptive Set Theory." Thesis, University of North Texas, 2015. https://digital.library.unt.edu/ark:/67531/metadc804953/.

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In this dissertation we study closure properties of pointclasses, scales on sets of reals and the models L[T2n], which are very natural canonical inner models of ZFC. We first characterize projective-like hierarchies by their associated ordinals. This solves a conjecture of Steel and a conjecture of Kechris, Solovay, and Steel. The solution to the first conjecture allows us in particular to reprove a strong partition property result on the ordinal of a Steel pointclass and derive a new boundedness principle which could be useful in the study of the cardinal structure of L(R). We then develop new methods which produce lightface scales on certain sets of reals. The methods are inspired by Jackson’s proof of the Kechris-Martin theorem. We then generalize the Kechris-Martin Theorem to all the Π12n+1 pointclasses using Jackson’s theory of descriptions. This in turns allows us to characterize the sets of reals of a certain initial segment of the models L[T2n]. We then use this characterization and the generalization of Kechris-Martin theorem to show that the L[T2n] are unique. This generalizes previous work of Hjorth. We then characterize the L[T2n] in term of inner models theory, showing that they actually are constructible models over direct limit of mice with Woodin cardinals, a counterpart to Steel’s result that the L[T2n+1] are extender models, and finally show that the generalized contiuum hypothesis holds in these models, solving a conjecture of Woodin.
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Dance, Cody. "Contributions to Descriptive Set Theory." Thesis, University of North Texas, 2016. https://digital.library.unt.edu/ark:/67531/metadc955115/.

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Assume AD+V=L(R). In the first chapter, let W^1_1 denote the club measure on \omega_1. We analyze the embedding j_{W^1_1}\restr HOD from the point of view of inner model theory. We use our analysis to answer a question of Jackson-Ketchersid about codes for ordinals less than \omega_\omega. In the second chapter, we provide an indiscernibles analysis for models of the form L[T_n,x]. We use our analysis to provide new proofs of the strong partition property on \delta^1_{2n+1}
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Longo, Cristiano. "Set theory for knowledge representation." Doctoral thesis, Università di Catania, 2012. http://hdl.handle.net/10761/1031.

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The decision problem in set theory has been intensively investigated in the last decades, and decision procedures or proofs of undecidability have been provided for several quantified and unquantified fragments of set theory. In this thesis we study the decision problem for three novel quantified fragments of set theory, which allow the explicit manipulation of ordered pairs. We present a decision procedure for each language of this family, and prove that all of these procedures are optimal (in the sense that they run in nondeterministic polynomial-time) when restricted to formulae with quantifier nesting bounded by a constant. The expressive power of languages of this family is then measured in terms of set-theoretical constructs they allow to express. In addition, these languages can be profitably employed in knowledge representation, since they allow to express a large amount description logic constructs.
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Corson, Samuel M. "Applications of Descriptive Set Theory in Homotopy Theory." BYU ScholarsArchive, 2010. https://scholarsarchive.byu.edu/etd/2401.

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This thesis presents new theorems in homotopy theory, in particular it generalizes a theorem of Saharon Shelah. We employ a technique used by Janusz Pawlikowski to show that certain Peano continua have a least nontrivial homotopy group that is finitely presented or of cardinality continuum. We also use this technique to give some relative consistency results.
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Popham, S. J. "Some studies in 'finitary' set theory." Thesis, University of Bristol, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.372022.

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Fernandes, Arias A. "The exceptional set in Nevanlinna theory." Thesis, Imperial College London, 1985. http://hdl.handle.net/10044/1/37689.

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Barton, Neil. "Executing Gödel's programme in set theory." Thesis, Birkbeck (University of London), 2017. http://bbktheses.da.ulcc.ac.uk/201/.

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The study of set theory (a mathematical theory of infinite collections) has garnered a great deal of philosophical interest since its development. There are several reasons for this, not least because it has a deep foundational role in mathematics; any mathematical statement (with the possible exception of a few controversial examples) can be rendered in set-theoretic terms. However, the fruitfulness of set theory has been tempered by two difficult yet intriguing philosophical problems: (1.) the susceptibility of naive formulations of sets to contradiction, and (2.) the inability of widely accepted set-theoretic axiomatisations to settle many natural questions. Both difficulties have lead scholars to question whether there is a single, maximal Universe of sets in which all set-theoretic statements are determinately true or false (often denoted by ‘V ’). This thesis illuminates this discussion by showing just what is possible on the ‘one Universe’ view. In particular, we show that there are deep relationships between responses to (1.) and the possible tools that can be used in resolving (2.). We argue that an interpretation of extensions of V is desirable for addressing (2.) in a fruitful manner. We then provide critical appraisal of extant philosophical views concerning (1.) and (2.), before motivating a strong mathematical system (known as‘Morse-Kelley’ class theory or ‘MK’). Finally we use MK to provide a coding of discourse involving extensions of V , and argue that it is philosophically virtuous. In more detail, our strategy is as follows: Chapter I (‘Introduction’) outlines some reasons to be interested in set theory from both a philosophical and mathematical perspective. In particular, we describe the current widely accepted conception of set (the ‘Iterative Conception’) on which sets are formed successively in stages, and remark that set-theoretic questions can be resolved on the basis of two dimensions: (i) how ‘high’ V is (i.e. how far we go in forming stages), and (ii) how ‘wide’ V is (i.e. what sets are formed at successor stages). We also provide a very coarse-grained characterisation of the set-theoretic paradoxes and remark that extensions of universes in both height and width are relevant for our understanding of (1.) and (2.). We then present the different motivations for holding either a ‘one Universe’ or ‘many universes’ view of the subject matter of set theory, and argue that there is a stalemate in the dialectic. Instead we advocate filling out each view in its own terms, and adopt the ‘one Universe’ view for the thesis. Chapter II (‘G¨odel’s Programme’) then explains the Universist project for formulating and justifying new axioms concerning V . We argue that extensions of V are relevant to both aspects of G¨odel’s Programme for resolving independence. We also identify a ‘Hilbertian Challenge’ to explain how we should interpret extensions of V , given that we wish to use discourse that makes apparent reference to such nonexistent objects. Chapter III (‘Problematic Principles’) then lends some mathematical precision to the coarse-grained outline of Chapter I, examining mathematical discourse that seems to require talk of extensions of V . Chapter IV (‘Climbing above V ?’), examines some possible interpretations of height extensions of V . We argue that several such accounts are philosophically problematic. However, we point out that these difficulties highlight two constraints on resolution of the Hilbertian Challenge: (i) a Foundational Constraint that we do not appeal to entities not representable using sets from V , and (ii) an Ontological Constraint to interpret extensions of V in such a way that they are clearly different from ordinary sets. 5 Chapter V (‘Broadening V ’s Horizons?’), considers interpretations of width extensions. Again, we argue that many of the extant methods for interpreting this kind of extension face difficulties. Again, however, we point out that a constraint is highlighted; a Methodological Constraint to interpret extensions of V in a manner that makes sense of our naive thinking concerning extensions, and links this thought to truth in V . We also note that there is an apparent tension between the three constraints. Chapter VI (‘A Theory of Classes’) changes tack, and provides a positive characterisation of apparently problematic ‘proper classes’ through the use of plural quantification. It is argued that such a characterisation of proper class discourse performs well with respect to the three constraints, and motivates the use of a relatively strong class theory (namely MK). Chapter VII (‘V -logic and Resolution’) then puts MK to work in interpreting extensions of V . We first expand our logical resources to a system called V -logic, and show how discourse concerning extensions can be thereby represented. We then show how to code the required amount of V -logic usingMK. Finally, we argue that such an interpretation performs well with respect to the three constraints. Chapter VIII (‘Conclusions’) reviews the thesis and makes some points regarding the exact dialectical situation. We argue that there are many different philosophical lessons that one might take from the thesis, and are clear that we do not commit ourselves to any one such conclusion. We finally provide some open questions and indicate directions for future research, remarking that the thesis opens the way for new and exciting philosophical and mathematical discussion.
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Ahmed, Shehzad. "Progressive Ideals in Combinatorial Set Theory." Ohio University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1554379497651916.

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Books on the topic "Set Theory"

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Bartoszyński, Tomek, and Marion Scheepers, eds. Set Theory. Providence, Rhode Island: American Mathematical Society, 1996. http://dx.doi.org/10.1090/conm/192.

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Di Prisco, Carlos Augusto, Jean A. Larson, Joan Bagaria, and A. R. D. Mathias, eds. Set Theory. Dordrecht: Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-015-8988-8.

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Bagaria, Joan, and Stevo Todorcevic, eds. Set Theory. Basel: Birkhäuser Basel, 2006. http://dx.doi.org/10.1007/3-7643-7692-9.

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Schindler, Ralf. Set Theory. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06725-4.

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Jech, Thomas. Set Theory. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-662-22400-7.

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Vaught, Robert L. Set Theory. Boston, MA: Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-0835-8.

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Dasgupta, Abhijit. Set Theory. New York, NY: Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4614-8854-5.

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Hausdorff, Felix. Set theory. 4th ed. New York, NY: Chelsea House Publishers, 1991.

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Pawar, Akhilesh. Set Theory. New Delhi, India: Campus Books International, 2012.

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Jech, Thomas J. Set theory. 3rd ed. Berlin: Springer, 2002.

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Book chapters on the topic "Set Theory"

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Devlin, Keith. "Set theory." In Sets, Functions and Logic, 52–72. Boston, MA: Springer US, 1992. http://dx.doi.org/10.1007/978-1-4899-2965-5_2.

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Löffler, Andreas, and Lutz Kruschwitz. "Set Theory." In Springer Texts in Business and Economics, 15–28. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-20103-6_2.

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Tao, Terence. "Set theory." In Texts and Readings in Mathematics, 33–73. Singapore: Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-1789-6_3.

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Pahl, Peter Jan, and Rudolf Damrath. "Set Theory." In Mathematical Foundations of Computational Engineering, 31–58. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-56893-0_2.

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Duşa, Adrian. "Set Theory." In QCA with R, 47–60. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-75668-4_3.

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Hall, Cordelia, and John O’Donnell. "Set Theory." In Discrete Mathematics Using a Computer, 111–27. London: Springer London, 2000. http://dx.doi.org/10.1007/978-1-4471-3657-6_4.

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Bishop, Errett, and Douglas Bridges. "Set Theory." In Grundlehren der mathematischen Wissenschaften, 67–80. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-642-61667-9_4.

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Pudlák, Pavel. "Set Theory." In Springer Monographs in Mathematics, 157–253. Heidelberg: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00119-7_3.

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Lavrov, Igor, Larisa Maksimova, and Giovanna Corsi. "Set theory." In Problems in Set Theory, Mathematical Logic and the Theory of Algorithms, 3–49. Boston, MA: Springer US, 2003. http://dx.doi.org/10.1007/978-1-4615-0185-5_1.

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Lavrov, Igor, Larisa Maksimova, and Giovanna Corsi. "Set theory." In Problems in Set Theory, Mathematical Logic and the Theory of Algorithms, 169–202. Boston, MA: Springer US, 2003. http://dx.doi.org/10.1007/978-1-4615-0185-5_4.

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Conference papers on the topic "Set Theory"

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Csajbok, Zoltan. "Partial approximative set theory: A generalization of the rough set theory." In 2010 International Conference of Soft Computing and Pattern Recognition (SoCPaR). IEEE, 2010. http://dx.doi.org/10.1109/socpar.2010.5686424.

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Moczydlowski, Wojciech. "A Dependent Set Theory." In 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007). IEEE, 2007. http://dx.doi.org/10.1109/lics.2007.7.

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Wu, Ming, De-lin Xia, and Pu-liu Yan. "Difference-similitude set theory." In Defense and Security, edited by Kevin L. Priddy. SPIE, 2005. http://dx.doi.org/10.1117/12.603140.

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Ming-Chun Wang, Zheng-Ou Wang, Ming Zhang, and Peng Yan. "Decision rule extraction method based on rough set theory and fuzzy set theory." In Proceedings of 2005 International Conference on Machine Learning and Cybernetics. IEEE, 2005. http://dx.doi.org/10.1109/icmlc.2005.1527312.

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Deepak, Sukheja, Javaid Ahmad Shah, Nagar Chetan, and Haryani Sharda. "New Decision-Making Process Based on Set Theory: Towards Application of Set Theory." In 2023 IEEE International Conference on ICT in Business Industry & Government (ICTBIG). IEEE, 2023. http://dx.doi.org/10.1109/ictbig59752.2023.10456045.

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Fu, Hao Cheng. "Supervaluationism and rough set theory." In 2012 IEEE International Conference on Granular Computing (GrC-2012). IEEE, 2012. http://dx.doi.org/10.1109/grc.2012.6468591.

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Hassan, Nasruddin, and Khaleed Alhazaymeh. "Vague soft expert set theory." In PROCEEDINGS OF THE 20TH NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES: Research in Mathematical Sciences: A Catalyst for Creativity and Innovation. AIP, 2013. http://dx.doi.org/10.1063/1.4801233.

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Abdel-Hamid, Ayman, Ossama Badawy, and Shreif Bahaa. "PA-SET: Privacy-aware SET protocol." In 2012 22nd International Conference on Computer Theory and Applications (ICCTA). IEEE, 2012. http://dx.doi.org/10.1109/iccta.2012.6523541.

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Lv Ruifeng, Wang Gang, and Wang Guoqing. "Applying rough set theory and fuzzy set theory to enterprise reference model classification and retrieval." In International Technology and Innovation Conference 2006 (ITIC 2006). IEE, 2006. http://dx.doi.org/10.1049/cp:20060935.

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Zhi Kong, Liqun Gao, Lifu Wang, and Yang Li. "Two operators in rough set theory." In 2007 46th IEEE Conference on Decision and Control. IEEE, 2007. http://dx.doi.org/10.1109/cdc.2007.4434180.

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Reports on the topic "Set Theory"

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Molinari, Francesca, Arie Beresteanu, and Ilya Molchanov. Partial identification using random set theory. Institute for Fiscal Studies, December 2010. http://dx.doi.org/10.1920/wp.cem.2010.4010.

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Gluckman, Albert G., and Aivars Celmins. Cost Effectiveness Analysis Using Fuzzy Set Theory. Fort Belvoir, VA: Defense Technical Information Center, December 1993. http://dx.doi.org/10.21236/ada274003.

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Esteva, Francesc. On Negations and Algebras in Fuzzy Set Theory. Fort Belvoir, VA: Defense Technical Information Center, March 1986. http://dx.doi.org/10.21236/ada604012.

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Goodman, I. R., and V. M. Bier. A Re-Examination of the Relationship between Fuzzy Set Theory and Probability Theory. Fort Belvoir, VA: Defense Technical Information Center, August 1991. http://dx.doi.org/10.21236/ada240243.

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Blasch, Erik, and Lang Hong. Set Theory Correlation Free Algorithm for HRRR Target Tracking. Fort Belvoir, VA: Defense Technical Information Center, January 1999. http://dx.doi.org/10.21236/ada385466.

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McPheron, Benjamin, and Josiah Kunz. Development of a Set of Pre-class Videos for Electromagnetic Theory. Purdue University, 2019. http://dx.doi.org/10.5703/1288284316886.

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Baader, Franz, Pavlos Marantidis, and Alexander Okhotin. Approximately Solving Set Equations. Technische Universität Dresden, 2016. http://dx.doi.org/10.25368/2022.227.

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Unification with constants modulo the theory ACUI of an associative (A), commutative (C) and idempotent (I) binary function symbol with a unit (U) corresponds to solving a very simple type of set equations. It is well-known that solvability of systems of such equations can be decided in polynomial time by reducing it to satisfiability of propositional Horn formulae. Here we introduce a modified version of this problem by no longer requiring all equations to be completely solved, but allowing for a certain number of violations of the equations. We introduce three different ways of counting the number of violations, and investigate the complexity of the respective decision problem, i.e., the problem of deciding whether there is an assignment that solves the system with at most l violations for a given threshold value l.
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Decolvenaere, Elizabeth, and Ann Elisabet Wills. DENSITY FUNCTIONAL THEORY APPLIED TO TRANSITION METAL ELEMENTS AND BINARIES: DEVELOPMENT APPLICATION AND RESULTS OF THE V-DM/16 TEST SET. Office of Scientific and Technical Information (OSTI), October 2016. http://dx.doi.org/10.2172/1562832.

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Wenner, Mark D. Dealing with Coordination Issues in Rural Development Projects: Game Theory Insights. Inter-American Development Bank, June 2007. http://dx.doi.org/10.18235/0011342.

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The purpose of this paper is to review the literature on coordination failures, apply game theory to coordination issues within selected rural development projects in order to develop a set of guidelines to avoid and minimize coordination failures. The ultimate aim is to promote development effectiveness by helping to improve project design. The intended audience is operational staff of the bank, staff in other donor agencies, policy makers, and academics interested in development effectiveness, enterprise development, and rural development. Case studies concern themselves with the rural agricultural and non-agricultural development in Latin America, but the theoretical insights can be applied to any sector or region of the world.
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Juden, Matthew, Tichaona Mapuwei, Till Tietz, Rachel Sarguta, Lily Medina, Audrey Prost, Macartan Humphreys, et al. Process Outcome Integration with Theory (POInT): academic report. Centre for Excellence and Development Impact and Learning (CEDIL), March 2023. http://dx.doi.org/10.51744/crpp5.

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This paper describes the development and testing of a novel approach to evaluating development interventions – the POInT approach. The authors used Bayesian causal modelling to integrate process and outcome data to generate insights about all aspects of the theory of change, including outcomes, mechanisms, mediators and moderators. They partnered with two teams who had evaluated or were evaluating complex development interventions: The UPAVAN team had evaluated a nutrition-sensitive agriculture intervention in Odisha, India, and the DIG team was in the process of evaluating a disability-inclusive poverty graduation intervention in Uganda. The partner teams’ theory of change were adapted into a formal causal model, depicted as a directed acyclic graph (DAG). The DAG was specified in the statistical software R, using the CausalQueries package, having extended the package to handle large models. Using a novel prior elicitation strategy to elicit beliefs over many more parameters than has previously been possible, the partner teams’ beliefs about the nature and strength of causal links in the causal model (priors) were elicited and combined into a single set of shared prior beliefs. The model was updated on data alone as well as on data plus priors to generate posterior models under different assumptions. Finally, the prior and posterior models were queried to learn about estimates of interest, and the relative role of prior beliefs and data in the combined analysis.
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