Results 21 to 30 of about 6,972,214 (183)
De Jongh's Theorem for Intuitionistic Zermelo-Fraenkel Set Theory [PDF]
, 2019 We prove that the propositional logic of intuitionistic set theory IZF is intuitionistic propositional logic IPC. More generally, we show that IZF has the de Jongh property with respect to every intermediate logic that is complete with respect to a class
Passmann, Robert
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On the Theories of Triangular Sets
Journal of Symbolic Computation, 1999 Different notions of triangular sets are presented. The relationship between these notions are studied. The main result is that four different existing notions of good triangular sets are equivalent.
Aubry, Philippe +2 more
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The Bulletin of Symbolic Logic, 2013 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.
OLIVER, ALEX, SMILEY, TIMOTHY
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Consequences of arithmetic for set theory
, 1993 In this paper, we consider certain cardinals in ZF (set theory without AC, the Axiom of Choice). In ZFC (set theory with AC), given any cardinals C and D, either C
Halbeisen, Lorenz, Shelah, Saharon
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Bulletin of Symbolic Logic, 2004 Ernst Friedrich Ferdinand Zermelo (1871–1953) transformed the set theory of Cantor and Dedekind in the first decade of the 20th century by incorporating the Axiom of Choice and providing a simple and workable axiomatization setting out generative set-existence principles.
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Out of Nowhere: Spacetime from causality: causal set theory [PDF]
, 2020 This is a chapter of the planned monograph "Out of Nowhere: The Emergence of Spacetime in Quantum Theories of Gravity", co-authored by Nick Huggett and Christian W\"uthrich and under contract with Oxford University Press.
Huggett, Nick, Wüthrich, Christian
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, 2023 We present a new fragment of axiomatic set theory for pure sets and for the iteration of power sets within given transitive sets. It turns out that this formal system admits an interesting hierarchy of models with true membership relation and with only finite or countably infinite ordinals.
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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
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Bulletin of Symbolic Logic, 2008 AbstractWe discuss the work of Paul Cohen in set theory and its influence, especially the background, discovery, development of forcing.
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