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Showing 1 to 20 of 158 for “"set theory"”.
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Some results in set theory
L'abstract è presente nell'allegato / the abstract is in the attachment
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SET THEORY FOR KNOWLEDGE REPRESENTATION
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 …
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Constructibility in impredicative set theory.
Massachusetts Institute of Technology. Dept. of Mathematics. Thesis. 1965. Ph.D.
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Tripos models of Internal Set Theory
… to make sense of models of E. Nelson’s Internal Set Theory (and hence of nonstandard analysis) in elementary toposes by exploiting the technology of tripos theory and Lawvere’s hyperdoctrines. A new doctrinal account of nonstandard phenomena is described, which avoids a few key restrictions in …
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Subsystems of set theory and analysis
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1967.
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Complexity hierarchies in generalized descriptive set theory
Within the framework of generalized descriptive set theory, we conduct a systematic analysis of several hierarchies of classes of sets and functions. At the level of sets, we study the Borel hierarchy, the difference hierarchy, and the Wadge hierarchy; at the level of functions, we examine the …
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A non-well-founded set theory (GST)
Open Restriction set for Item 19544 on 2020-11-02T17:15:11Z with date null by astein@illinois.edu.
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Pointwise ergodic theorems via descriptive set theory
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2024-05-01
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Independence and conservativity results for intuitionistic set theory
… realizability to intuitionistic Zermelo-Fraenkel set theory with two sorts, IZFN. In addition to separating Church's thesis with uniqueness condition from its general form in intuitionistic set theory, I also obtain several interesting corollaries. The interpretation repudiates a weak form of …
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An Account of the Development of Set Theory
Made available in DSpace on 2014-12-10T18:48:35Z (GMT). No. of bitstreams: 1 7514128.pdf: 11174849 bytes, checksum: a1737e2f81201f15ed6148eb4a3d49fb (MD5) Previous issue date: 1975
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Transfinite Sequences of Axiom Systems for Set Theory
Made available in DSpace on 2014-12-09T22:17:43Z (GMT). No. of bitstreams: 1 6808241.pdf: 1998340 bytes, checksum: d9b52b03ffc0b694a65007e65b1b0a0d (MD5) Previous issue date: 1967
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Coloring problems in combinatorics and descriptive set theory
… context and in the framework of descriptive set theory, with applications to topological dynamics and ergodic theory. This work consists of two parts, each of which is in turn split into a number of chapters. Although the individual chapters are largely independent from each other (with the …
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Axiomatization and Incompleteness in Arithmetic and Set Theory
… and Incompleteness in Arithmetic and Set Theory Wesley Duncan Wrigley I argue that are (at least) two distinct kinds of mathematical incompleteness. Part A of the thesis discusses Gödelian incompleteness, while Part B is concerned with set-theoretic incompleteness. Both parts are …
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An investment analysis model using fuzzy set theory
… and non-economic, tangible and intangible. Fuzzy set theory provides an alternative to probability theory for handling uncertainty, while at the same time being able to handle imprecision. It also provides a means of closing the gap between the human thought process and the computer, by enabling …
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Internal Set Theory and Euler's Introductio in Analysin Infinitorum
… (NSA); in particular, we will use Internal Set Theory, Edward Nelson's distinctive version of NSA. We will specifically examine Euler's proofs of the Euler formula, the Euler product, the Wallis product and the divergence of the harmonic series. All of these results have been proved in …
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Aspects of Large Cardinals (Set Theory, Logic, Measurable, Strongly Compact, Extendible)
This paper deals with three subjects in set theory. Chapter I concerns a categorical representation of measurable cardinals. The result answers Girard's presumption "The solution to make the order relation between dilators total will be connected to large cardinal axioms, if it exists" negatively. …
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A relatively small turing machine whose behavior is independent of set theory
Since the definition of the Busy Beaver function by Radó in 1962, an interesting open question has been what the smallest value of n for which BB(n) is independent of ZFC. Is this n approximately 10, or closer to 1,000,000, or is it unfathomably large? In this thesis, I show that it is at most …
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