Results 21 to 30 of about 3,715 (167)
Axioms, 2021 It is well known that Zermelo-Fraenkel Set Theory (ZF), despite its usefulness as a foundational theory for mathematics, has two unwanted features: it cannot be written down explicitly due to its infinitely many axioms, and it has a countable model due ...
Marcoen J. T. F. Cabbolet
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Mobile Information Systems, Volume 2022, Issue 1, 2022., 2022 The IoT refers to the linking of items to a network through message‐generating devices; in the connection process, communication and information circulation are carried out through the information dissemination medium to realize intelligent identification, tracking, supervision, and other functions.
Hongmei Xun +3 more
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Theoria, Volume 87, Issue 4, Page 986-1000, August 2021., 2021 Abstract Informally speaking, the categoricity of an axiom system means that its non‐logical symbols have only one possible interpretation that renders the axioms true. Although non‐categoricity has become ubiquitous in the second half of the twentieth century whether one looks at number theory, geometry or analysis, the first axiomatizations of such ...
Jouko Väänänen
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An Overview of Saharon Shelah's Contributions to Mathematical Logic, in Particular to Model Theory
Theoria, Volume 87, Issue 2, Page 349-360, April 2021., 2021 Abstract I will give a brief overview of Saharon Shelah's work in mathematical logic. I will focus on three transformative contributions Shelah has made: stability theory, proper forcing and PCF theory. The first is in model theory and the other two are in set theory.
Jouko Väänänen
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Ontologia disorientata agli oggetti: Processualità e transiti nella matematica contemporanea [PDF]
Kaiak, 2023 As well as playing a foundational role in mathematics, set theory formalises the possibility of working with collections of objects. Intuitive, vague and general before Cantor, the set-theoretic approach would assume a central role in twentieth-century ...
Nicola Turrini
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Black Holes and Complexity via Constructible Universe
Universe, 2020 The relation of randomness and classical algorithmic computational complexity is a vast and deep subject by itself. However, already, 1-randomness sequences call for quantum mechanics in their realization.
Jerzy Król, Paweł Klimasara
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Infinite sequential Nash equilibrium [PDF]
Logical Methods in Computer Science, 2013 In game theory, the concept of Nash equilibrium reflects the collective stability of some individual strategies chosen by selfish agents. The concept pertains to different classes of games, e.g. the sequential games, where the agents play in turn.
Stephane Le Roux
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On the structure of completely useful topologies
Applied General Topology, 2002 Let X be an arbitrary set. Then a topology t on X is completely useful if every upper semicontinuous linear preorder on X can be represented by an upper semicontinuous order preserving real-valued function.
Gianni Bosi, Gerhard Herden
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On the structure of classical realizability models of ZF [PDF]
, 2014 The technique of "classical realizability" is an extension of the method of "forcing"; it permits to extend the Curry-Howard correspondence between proofs and programs, to Zermelo-Fraenkel set theory and to build new models of ZF, called "realizability ...
Krivine, Jean-Louis
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Uncountable dichromatic number without short directed cycles
Journal of Graph Theory, Volume 94, Issue 1, Page 113-116, May 2020., 2020 Abstract Hajnal and Erdős proved that a graph with uncountable chromatic number cannot avoid short cycles, it must contain, for example, C4 (among other obligatory subgraphs). It was shown recently by Soukup that, in contrast of the undirected case, it is consistent that for any n<ω there exists an uncountably dichromatic digraph without directed ...
Attila Joó
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