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Mathematische Annalen, 1997 As is well known, some paradoxes arise through inadequate analysis of the meanings of terms in a language, an adequate analysis showing that the paradoxes arise through a lack of separation of an object theory and a metatheory. Under such an adequate analysis in which parts of the metatheory are modelled in the object theory, the paradoxes give way to ...
OLIVER DEISER, DEISER, OLIVER
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A Formal System of Axiomatic Set Theory in Coq
IEEE Access, 2020 Formal verification technology has been widely applied in the fields of mathematics and computer science. The formalization of fundamental mathematical theories is particularly essential.
Tianyu Sun, Wensheng Yu
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Arrow of Time in Quantum Mechanics and Set Theory [PDF]
EntropyThe set-theory twist of quantum mechanics uncovers forcing in axiomatic Zermelo–Fraenkel set theory as a viable tool to understand the singularities in a physical spacetime and serves as a link between the quantum and classical worlds. The random forcing
Jerzy Król
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Finite Arithmetic Axiomatization for the Basis of Hyperrational Non-Standard Analysis
Axioms, 2021 The standard elementary number theory is not a finite axiomatic system due to the presence of the induction axiom scheme. Absence of a finite axiomatic system is not an obstacle for most tasks, but may be considered as imperfect since the induction is ...
Yuri N. Lovyagin, Nikita Yu. Lovyagin
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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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A Logical Framework for Set Theories [PDF]
Electronic Proceedings in Theoretical Computer Science, 2012 Axiomatic set theory is almost universally accepted as the basic theory which provides the foundations of mathematics, and in which the whole of present day mathematics can be developed.
Arnon Avron
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“Mathematics is the Logic of the Infinite”: Zermelo’s Project of Infinitary Logic
Studies in Logic, Grammar and Rhetoric, 2021 In this paper I discuss Ernst Zermelo’s ideas concerning the possibility of developing a system of infinitary logic that, in his opinion, should be suitable for mathematical inferences. The presentation of Zermelo’s ideas is accompanied with some remarks
Pogonowski Jerzy
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Axiomatic Foundations of Anisotropy-Based and Spectral Entropy Analysis: A Comparative Study
Mathematics, 2023 An axiomatic development of control systems theory can systematize important concepts. The current research article is dedicated to the investigation and comparison of two axiomatic approaches to the analysis of discrete linear time-invariant systems ...
Victor A. Boichenko +2 more
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Logic, Game Theory, and Social Choice: What Do They Have in Common?
Axioms, 2022 The answer to the question above is that in all these domains axiomatic characterizations are given of, respectively, mathematical reasoning, certain notions from game theory, and certain social choice rules.
Harrie de Swart
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Towards an axiomatic formulation of noncommutative quantum field theory. II
Nuclear Physics B, 2020 Classical results of the axiomatic quantum field theory – irreducibility of the set of field operators, Reeh and Schlieder's theorems and generalized Haag's theorem are proven in SO(1,1) invariant quantum field theory, of which an important example is ...
M. Chaichian +2 more
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