Every Countable Model of Arithmetic or Set Theory has a Pointwise-Definable End Extension
KRITERION – Journal of PhilosophyAbstract According to the math tea argument, there must be real numbers that we cannot describe or define, because there are uncountably many real numbers, but only countably many definitions. And yet, the existence of pointwise-definable models of set theory, in which every individual is definable without ...
Hamkins, Joel David
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Gödel Mathematics Versus Hilbert Mathematics. II Logicism and Hilbert Mathematics, the Identification of Logic and Set Theory, and Gödel’s 'Completeness Paper' (1930) [PDF]
, 2023 The previous Part I of the paper discusses the option of the Gödel incompleteness statement (1931: whether “Satz VI” or “Satz X”) to be an axiom due to the pair of the axiom of induction in arithmetic and the axiom of infinity in set theory after ...
Penchev, Vasil
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Provability logic: models within models in Peano Arithmetic [PDF]
, 2023 In 1994 Jech gave a model-theoretic proof of Godel's second incompleteness theorem for Zermelo-Fraenkel set theory in the following form: ZF does not prove that ZF has a model. Kodarski showed that Jech's proof can be adapted to Peano Arithmetic with the
Berarducci, A, Mamino, M
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Evaluating investments in advanced manufacturing technology: A fuzzy set theory approach [PDF]
, 2001 In this paper, a model for the evaluation of investments in advanced manufacturing technology is developed. Many authors have called for an integration of financial and non-financial factors in such evaluations and this paper demonstrates that it is ...
Dugdale, D, Abdel-Kader, MG
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On expandability of models of arithmetic and set theory to models of weak second-order theories [PDF]
Fundamenta Mathematicae, 1984 Answering two questions of Bell, Marek and Srebrny the author shows that for any consistent extension T of \(\Sigma^ 1_ 1\)-PA there is no class \(\Phi\) of \(L_{\infty \omega}\) sentences such that for all \({\mathfrak M}\vDash PA\), \({\mathfrak M}\) is expandable to a model of T iff \({\mathfrak M}\vDash \phi\), and the same if we replace PA by ZF ...
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Quantum recurrences and the arithmetic of Floquet dynamics [PDF]
QuantumThe Poincaré recurrence theorem shows that conservative systems in a bounded region of phase space eventually return arbitrarily close to their initial state after a finite amount of time.
Amit Anand +3 more
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Tecnura, 2014 In the biological environment, there has been created epidemiological models that attempt to explain the spread dynamics of an epidemic in a population to predict the behavior of possible epidemics that can affect humanity.
Pedro Guevara López +3 more
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Product Space Models of Correlation: Between Noise Stability and Additive Combinatorics
Discrete Analysis, 2018 Product Space Models of Correlation: Between Noise Stability and Additive Combinatorics, Discrete Analysis 2018:20, 63 pp. Szemerédi's theorem states that for every positive integer $\ell$ and every $\mu>0$ there exists $N$ such that every subset of ...
Jan Hązła +2 more
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A Mathematical Model of Quantum Computer by Both Arithmetic and Set Theory
SSRN Electronic Journal, 2020 A practical viewpoint links reality, representation, and language to calculation by the concept of Turing (1936) machine being the mathematical model of our computers. After the Gödel incompleteness theorems (1931) or the insolvability of the so-called halting problem (Turing 1936; Church 1936) as to a classical machine of Turing, one of the simplest ...
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Linear Equation Systems Under Uncertainty: Applications to Multiproduct Market Equilibrium
MathematicsMarket equilibrium models are essential tools within classical economic theory for analyzing the interaction between supply and demand. However, traditional formulations are often based on deterministic relationships and assume the existence of perfect ...
Vicente Liern +2 more
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