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Set Theory: Boolean-Valued Models and Independence Proofs
TLDR
In this paper, the authors present a list of problems with Boolean and Heyting algebra-valued models: first steps, forcing and some independent proofs, group actions on V(B) and the Independence of the Axiom of Choice, generic Ultrafilters and Transitive Models of ZFC.Abstract:
Foreword Preface List of Problems 0 Boolean and Heyting Algebras: The Essentials 1 Boolean-Valued Models: First Steps 2 Forcing and Some Independece Proofs 3 Group Actions on V(B) and the Independence of the Axiom of Choice 4 Generic Ultrafilters and Transitive Models of ZFC 5 Cardinal Collapsing, Boolean Isomorphism and Applications to the Theory of Boolean Algebras 6 Iterated Boolean Extensions, Martin's Axiom and Souslin's Hypothesis 7 Boolean-Valued Analysis 8 Intuitionistic Set Theory and Heyting-Algebra-Valued Models Appendix Boolean- and Heyting-Algebra-Valued Models as Categories Historical Notes Bibliography Index of Symbols Index of Termsread more
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Transfinite cardinals in paraconsistent set theory
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The algebra of conditional sets and the concepts of conditional topology and compactness
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Logic for Artificial Intelligence: A Rasiowa–Pawlak School Perspective
TL;DR: A great importance in the studies of the Rasiowa–Pawlak school is assigned to the search for optimal tools for reasoning about complex vague concepts, construction of knowledge representation systems, reasoning about knowledge as well as for the application of logics in learning, communication, perception, planning, action, cooperation, and competition.
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Generalized algebra-valued models of set theory
Benedikt Löwe,Sourav Tarafder +1 more
TL;DR: A model of a paraconsistent logic that validates all axioms of the negation-free fragment of Zermelo-Fraenkel set theory is shown.
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A beginner's guide to forcing
TL;DR: In this article, an expository paper aimed at the reader without much background in set theory or logic, gives an overview of Cohen's proof (via forcing) of the independence of the continuum hypothesis.