Results 41 to 50 of about 3,715 (167)
The Essence of Intuitive Set Theory [PDF]
, 2001 Intuitive Set Theory (IST) is defined as the theory we get, when we add Axiom of Monotonicity and Axiom of Fusion to Zermelo-Fraenkel set theory. In IST, Continuum Hypothesis is a theorem, Axiom of Choice is a theorem, Skolem paradox does not appear ...
Nambiar, Kannan
core +2 more sources
Noûs, Volume 58, Issue 2, Page 306-332, June 2024.Abstract Mathematical pluralism can take one of three forms: (1) every consistent mathematical theory consists of truths about its own domain of individuals and relations; (2) every mathematical theory, consistent or inconsistent, consists of truths about its own (possibly uninteresting) domain of individuals and relations; and (3) the principal ...
Edward N. Zalta
wiley +1 more source
Contractive Maps in Locally Transitive Relational Metric Spaces
The Scientific World Journal, Volume 2014, Issue 1, 2014., 2014 Some fixed point results are given for a class of Meir‐Keeler contractive maps acting on metric spaces endowed with locally transitive relations. Technical connections with the related statements due to Berzig et al. (2014) are also being discussed.
Mihai Turinici +4 more
wiley +1 more source
Weyl and two kinds of potential domains
Noûs, Volume 58, Issue 2, Page 409-430, June 2024.Abstract According to Weyl, “‘inexhaustibility’ is essential to the infinite”. However, he distinguishes two kinds of inexhaustible, or merely potential, domains: those that are “extensionally determinate” and those that are not. This article clarifies Weyl's distinction and explains its enduring logical and philosophical significance.
Laura Crosilla, Øystein Linnebo
wiley +1 more source
Homeomorphisms of Compact Sets in Certain Hausdorff Spaces
International Journal of Mathematics and Mathematical Sciences, Volume 2011, Issue 1, 2011., 2011 We construct a class of Hausdorff spaces (compact and noncompact) with the property that nonempty compact subsets of these spaces that have the same cardinality are homeomorphic. Also, it is shown that these spaces contain compact subsets that are infinite.
Arthur D. Grainger, Vladimir Mityushev
wiley +1 more source
Wetzel families and the continuum
Journal of the London Mathematical Society, Volume 109, Issue 6, June 2024.Abstract We provide answers to a question brought up by Erdős about the construction of Wetzel families in the absence of the continuum hypothesis: A Wetzel family is a family F$\mathcal {F}$ of entire functions on the complex plane which pointwise assumes fewer than |F|$\vert \mathcal {F} \vert$ values.
Jonathan Schilhan, Thilo Weinert
wiley +1 more source
Small sets in convex geometry and formal independence over ZFC
Abstract and Applied Analysis, Volume 2005, Issue 5, Page 469-488, 2005., 2005 To each closed subset S of a finite‐dimensional Euclidean space corresponds a σ‐ideal of sets 𝒥 (S) which is σ‐generated over S by the convex subsets of S. The set‐theoretic properties of this ideal hold geometric information about the set. We discuss the relation of reducibility between convexity ideals and the connections between convexity ideals and
Menachem Kojman
wiley +1 more source
ISABELLE - THE NEXT 700 THEOREM PROVERS [PDF]
, 1988 Isabelle is a generic theorem prover, designed for interactive reasoning in a variety of formal theories. At present it provides useful proof procedures for Constructive Type Theory, various first-order logics, Zermelo-Fraenkel set theory, and higher ...
PAULSON, LC
core +1 more source
Encoding TLA+ set theory into many-sorted first-order logic [PDF]
, 2015 We present an encoding of Zermelo-Fraenkel set theory into many-sorted first-order logic, the input language of state-of-the-art SMT solvers.
Merz, Stephan, Vanzetto, Hernán
core +3 more sources
Binary Relations as a Foundation of Mathematics [PDF]
, 2007 We describe a theory for binary relations in the Zermelo-Fraenkel style. We choose for ZFCU, a variant of ZFC Set theory in which the Axiom of Foundation is replaced by an axiom allowing for non-wellfounded sets.
Kuper, J.
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