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Artykuły w czasopismach na temat „Set Theory”

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Autor: Grafiati

Data publikacji: 4 czerwca 2021

Data aktualizacji: 5 października 2024

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1

Farah, Ilijas, Sy-David Friedman, Menachem Magidor i W. Hugh Woodin. "Set Theory". Oberwolfach Reports 11, nr 1 (2014): 91–144. http://dx.doi.org/10.4171/owr/2014/02.

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2

Farah, Ilijas, Sy-David Friedman, Ralf-Dieter Schindler i W. Hugh Woodin. "Set Theory". Oberwolfach Reports 14, nr 1 (2.01.2018): 527–89. http://dx.doi.org/10.4171/owr/2017/11.

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3

Farah, Ilijas, Ralf-Dieter Schindler, Dima Sinapova i W. Hugh Woodin. "Set Theory". Oberwolfach Reports 17, nr 2 (1.07.2021): 797–855. http://dx.doi.org/10.4171/owr/2020/14.

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4

Neidhöfer, Christoph. "Set Theory". Zeitschrift der Gesellschaft für Musiktheorie [Journal of the German-Speaking Society of Music Theory] 1–2, nr 2/2–3 (2005): 219–27. http://dx.doi.org/10.31751/530.

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5

Merrell, Patrick. "Set Theory". Scientific American 295, nr 6 (grudzień 2006): 110. http://dx.doi.org/10.1038/scientificamerican1206-110.

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6

Farah, Ilijas, Ralf Schindler, Dima Sinapova i W. Hugh Woodin. "Set Theory". Oberwolfach Reports 19, nr 1 (10.03.2023): 79–106. http://dx.doi.org/10.4171/owr/2022/2.

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7

Hajek, P., i Z. Hanikova. "Interpreting lattice-valued set theory in fuzzy set theory". Logic Journal of IGPL 21, nr 1 (18.07.2012): 77–90. http://dx.doi.org/10.1093/jigpal/jzs023.

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8

Jiang, Jingying. "From Set Theory to the Axiomatization of Set Theory". Highlights in Science, Engineering and Technology 88 (29.03.2024): 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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9

Takeuti, Gaisi. "Proof theory and set theory". Synthese 62, nr 2 (luty 1985): 255–63. http://dx.doi.org/10.1007/bf00486049.

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10

Slater, Hartley. "Aggregate Theory Versus Set Theory". Philosophia Scientae, nr 9-2 (1.11.2005): 131–44. http://dx.doi.org/10.4000/philosophiascientiae.530.

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11

Potter, M. D. "Iterative Set Theory". Philosophical Quarterly 43, nr 171 (kwiecień 1993): 178. http://dx.doi.org/10.2307/2220368.

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12

Lord, Nick, John C. Morgan, D. N. Dikranjan, I. R. Prodanov i L. N. Stoyanov. "Point Set Theory". Mathematical Gazette 75, nr 473 (październik 1991): 397. http://dx.doi.org/10.2307/3619553.

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13

Shelah, Saharon. "Applying Set Theory". Axioms 10, nr 4 (30.11.2021): 329. http://dx.doi.org/10.3390/axioms10040329.

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We prove some results in set theory as applied to general topology and model theory. In particular, we study ℵ1-collectionwise Hausdorff, Chang Conjecture for logics with Malitz-Magidor quantifiers and monadic logic of the real line by odd/even Cantor sets.

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14

Fletcher, Peter. "Nonstandard set theory". Journal of Symbolic Logic 54, nr 3 (wrzesień 1989): 1000–1008. http://dx.doi.org/10.2307/2274759.

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AbstractNonstandard set theory is an attempt to generalise nonstandard analysis to cover the whole of classical mathematics. Existing versions (Nelson, Hrbáček, Kawai) are unsatisfactory in that the unlimited idealisation principle conflicts with the wish to have a full theory of external sets.I re-analyse the underlying requirements of nonstandard set theory and give a new formal system, stratified nonstandard set theory, which seems to meet them better than the other versions.

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15

Kirby, Laurence. "Finitary Set Theory". Notre Dame Journal of Formal Logic 50, nr 3 (lipiec 2009): 227–44. http://dx.doi.org/10.1215/00294527-2009-009.

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16

OLIVER, ALEX, i TIMOTHY SMILEY. "CANTORIAN SET THEORY". Bulletin of Symbolic Logic 24, nr 4 (grudzień 2018): 393–451. http://dx.doi.org/10.1017/bsl.2018.10.

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AbstractAlmost all set theorists pay at least lip service to Cantor’s definition of a set as a collection of many things into one whole; but empty and singleton sets do not fit with it. Adapting Dana Scott’s axiomatization of the cumulative theory of types, we present a ‘Cantorian’ system which excludes these anomalous sets. We investigate the consequences of their omission, examining their claim to a place on grounds of convenience, and asking whether their absence is an obstacle to the theory’s ability to represent ordered pairs or to support the arithmetization of analysis or the development of the theory of cardinals and ordinals.

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17

Titani, Satoko, i Haruhiko Kozawa. "Quantum Set Theory". International Journal of Theoretical Physics 42, nr 11 (listopad 2003): 2575–602. http://dx.doi.org/10.1023/b:ijtp.0000005977.55748.e4.

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18

Maji, P. K., R. Biswas i A. R. Roy. "Soft set theory". Computers & Mathematics with Applications 45, nr 4-5 (luty 2003): 555–62. http://dx.doi.org/10.1016/s0898-1221(03)00016-6.

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19

Nambiar, K. K. "Real set theory". Computers & Mathematics with Applications 38, nr 7-8 (październik 1999): 167–71. http://dx.doi.org/10.1016/s0898-1221(99)00247-3.

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20

Nambiar, K. K. "Intuitive set theory". Computers & Mathematics with Applications 39, nr 1-2 (styczeń 2000): 183–85. http://dx.doi.org/10.1016/s0898-1221(99)00322-3.

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21

Nishimura, Hirokazu. "Empirical set theory". International Journal of Theoretical Physics 32, nr 8 (sierpień 1993): 1293–321. http://dx.doi.org/10.1007/bf00675196.

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22

Strauss, Paul. "Arithmetical Set Theory". Studia Logica 50, nr 2 (czerwiec 1991): 343–50. http://dx.doi.org/10.1007/bf00370192.

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23

Shehtman, V. "Review: Set Theory". Journal of Logic and Computation 15, nr 1 (1.02.2005): 75–76. http://dx.doi.org/10.1093/logcom/exh039.

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24

Reinhardt, William N. "Epistemic set theory." Notre Dame Journal of Formal Logic 29, nr 2 (marzec 1988): 216–28. http://dx.doi.org/10.1305/ndjfl/1093637872.

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25

Tom Leinster. "Rethinking Set Theory". American Mathematical Monthly 121, nr 5 (2014): 403. http://dx.doi.org/10.4169/amer.math.monthly.121.05.403.

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26

Losada, Catherine. "Around set theory". Journal of Mathematics and Music 4, nr 3 (listopad 2010): 175–81. http://dx.doi.org/10.1080/17459737.2010.531214.

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27

Zakharov, V. K. "Local set theory". Mathematical Notes 77, nr 1-2 (styczeń 2005): 177–93. http://dx.doi.org/10.1007/s11006-005-0019-x.

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28

Lehmann, Ingo, Richard Weber i Hans Jürgen Zimmermann. "Fuzzy set theory". Operations-Research-Spektrum 14, nr 1 (marzec 1992): 1–9. http://dx.doi.org/10.1007/bf01783496.

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29

Zimmermann, H. J. "Fuzzy set theory". Wiley Interdisciplinary Reviews: Computational Statistics 2, nr 3 (16.04.2010): 317–32. http://dx.doi.org/10.1002/wics.82.

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30

Barr, Michael. "Fuzzy Set Theory and Topos Theory". Canadian Mathematical Bulletin 29, nr 4 (1.12.1986): 501–8. http://dx.doi.org/10.4153/cmb-1986-079-9.

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AbstractThe relation between the categories of Fuzzy Sets and that of Sheaves is explored and the precise connection between them is explicated. In particular, it is shown that if the notion of fuzzy sets is further fuzzified by making equality (as well as membership) fuzzy, the resultant categories are indeed toposes.

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31

Musès, C. "System Theory and Deepened Set Theory". Kybernetes 22, nr 6 (czerwiec 1993): 91–99. http://dx.doi.org/10.1108/eb005994.

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32

KELLY, KEVIN T. "Learning Theory and Descriptive Set Theory". Journal of Logic and Computation 3, nr 1 (1993): 27–45. http://dx.doi.org/10.1093/logcom/3.1.27.

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33

Flagg, R. C. "Epistemic set theory is a conservative extension of intuitionistic set theory". Journal of Symbolic Logic 50, nr 4 (grudzień 1985): 895–902. http://dx.doi.org/10.2307/2273979.

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In [6] Gödel observed that intuitionistic propositional logic can be interpreted in Lewis's modal logic (S4). The idea behind this interpretation is to regard the modal operator □ as expressing the epistemic notion of “informal provability”. With the work of Shapiro [12], Myhill [10], Goodman [7], [8], and Ščedrov [11] this simple idea has developed into a successful program of integrating classical and intuitionistic mathematics.There is one question quite central to the above program that has remained open. Namely:Does Ščedrov's extension of the Gödel translation to set theory provide a faithful interpretation of intuitionistic set theory into epistemic set theory?In the present paper we give an affirmative answer to this question.The main ingredient in our proof is the construction of an interpretation of epistemic set theory into intuitionistic set theory which is inverse to the Gödel translation. This is accomplished in two steps. First we observe that Funayama's theorem is constructively provable and apply it to the power set of 1. This provides an embedding of the set of propositions into a complete topological Boolean algebra . Second, in a fashion completely analogous to the construction of Boolean-valued models of classical set theory, we define the -valued universe V(). V() gives a model of epistemic set theory and, since we use a constructive metatheory, this provides an interpretation of epistemic set theory into intuitionistic set theory.

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34

Terui, Kazushige. "Light Affine Set Theory: A Naive Set Theory of Polynomial Time". Studia Logica 77, nr 1 (czerwiec 2004): 9–40. http://dx.doi.org/10.1023/b:stud.0000034183.33333.6f.

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35

Jones, Robert. "Elementary set theory with a universal set". Mathematical Intelligencer 29, nr 3 (czerwiec 2007): 71–73. http://dx.doi.org/10.1007/bf02985697.

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36

Steggles, I., i Robert L. Vaught. "Set Theory, an Introduction". Mathematical Gazette 71, nr 458 (grudzień 1987): 324. http://dx.doi.org/10.2307/3617077.

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37

Abbott, Steve, i Iain T. Adamson. "A Set Theory Workbook". Mathematical Gazette 83, nr 496 (marzec 1999): 168. http://dx.doi.org/10.2307/3618735.

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38

Kilmister, C. W., Karel Hrbacek i Thomas Jech. "Introduction to Set Theory". Mathematical Gazette 84, nr 499 (marzec 2000): 173. http://dx.doi.org/10.2307/3621546.

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39

Kanamori, Akihiro. "Gödel and Set Theory". Bulletin of Symbolic Logic 13, nr 2 (czerwiec 2007): 153–88. http://dx.doi.org/10.2178/bsl/1185803804.

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Kurt Gödel (1906–1978) with his work on the constructible universeLestablished the relative consistency of the Axiom of Choice (AC) and the Continuum Hypothesis (CH). More broadly, he ensured the ascendancy of first-order logic as the framework and a matter of method for set theory and secured the cumulative hierarchy view of the universe of sets. Gödel thereby transformed set theory and launched it with structured subject matter and specific methods of proof. In later years Gödel worked on a variety of set theoretic constructions and speculated about how problems might be settled with new axioms. We here chronicle this development from the point of view of the evolution of set theory as a field of mathematics. Much has been written, of course, about Gödel's work in set theory, from textbook expositions to the introductory notes to his collected papers. The present account presents an integrated view of the historical and mathematical development as supported by his recently published lectures and correspondence. Beyond the surface of things we delve deeper into the mathematics. What emerges are the roots and anticipations in work of Russell and Hilbert, and most prominently the sustained motif of truth as formalizable in the “next higher system”. We especially work at bringing out how transforming Gödel's work was for set theory. It is difficult now to see what conceptual and technical distance Gödel had to cover and how dramatic his re-orientation of set theory was.

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40

Kanamori, Akihiro. "Cohen and Set Theory". Bulletin of Symbolic Logic 14, nr 3 (wrzesień 2008): 351–78. http://dx.doi.org/10.2178/bsl/1231081371.

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41

Kanamori, Akihiro. "Bernays and Set Theory". Bulletin of Symbolic Logic 15, nr 1 (marzec 2009): 43–69. http://dx.doi.org/10.2178/bsl/1231081769.

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42

FUCHINO, Sakaé. "Mathematics and Set Theory:". Journal of the Japan Association for Philosophy of Science 46, nr 1 (2018): 33–47. http://dx.doi.org/10.4288/kisoron.46.1_33.

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43

Kirby, Laurence. "Bounded finite set theory". Mathematical Logic Quarterly 67, nr 2 (maj 2021): 149–63. http://dx.doi.org/10.1002/malq.202000056.

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44

Morgan. "TRANSCENDENTAL POINT SET THEORY". Real Analysis Exchange 24, nr 1 (1998): 29. http://dx.doi.org/10.2307/44152910.

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45

Green, Frederic. "Review of Set Theory". ACM SIGACT News 48, nr 3 (7.09.2017): 7–9. http://dx.doi.org/10.1145/3138860.3138863.

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46

Radu, C., i R. Wilkerson. "Using fuzzy set theory". IEEE Potentials 14, nr 5 (1996): 33–35. http://dx.doi.org/10.1109/45.481510.

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47

Hart, Joan E., Kenneth Kunen i Yiannis N. Moschovakis. "Notes on Set Theory." American Mathematical Monthly 103, nr 1 (styczeń 1996): 87. http://dx.doi.org/10.2307/2975227.

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48

KANAMORI, AKIHIRO. "ERDŐS AND SET THEORY". Bulletin of Symbolic Logic 20, nr 4 (grudzień 2014): 449–90. http://dx.doi.org/10.1017/bsl.2014.38.

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Paul Erdős (26 March 1913—20 September 1996) was a mathematicianpar excellencewhose results and initiatives have had a large impact and made a strong imprint on the doing of and thinking about mathematics. A mathematician of alacrity, detail, and collaboration, Erdős in his six decades of work moved and thought quickly, entertained increasingly many parameters, and wrote over 1500 articles, the majority with others. Hismodus operandiwas to drive mathematics through cycles of problem, proof, and conjecture, ceaselessly progressing and ever reaching, and hismodus vivendiwas to be itinerant in the world, stimulating and interacting about mathematics at every port and capital.

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49

JÄGER, GERHARD. "RELATIVIZING OPERATIONAL SET THEORY". Bulletin of Symbolic Logic 22, nr 3 (wrzesień 2016): 332–52. http://dx.doi.org/10.1017/bsl.2016.11.

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AbstractWe introduce a way of relativizing operational set theory that also takes care of application. After presenting the basic approach and proving some essential properties of this new form of relativization we turn to the notion of relativized regularity and to the system OST (LR) that extends OST by a limit axiom claiming that any set is element of a relativized regular set. Finally we show that OST (LR) is proof-theoretically equivalent to the well-known theory KPi for a recursively inaccessible universe.

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50

Yee, Jerry. "Set Theory: Nephrology ∩ Urology". Advances in Chronic Kidney Disease 22, nr 4 (lipiec 2015): 253–55. http://dx.doi.org/10.1053/j.ackd.2015.05.001.

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