Results 261 to 270 of about 3,387,563 (289)
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Logic in Computer Science
In the setting of constructive reverse mathematics, we analyse the downward Löwenheim-Skolem (DLS) theorem of first-order logic, stating that every infinite model has a countable elementary submodel. Refining the well-known equivalence of the DLS theorem
Dominik Kirst, Haoyi Zeng
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In the setting of constructive reverse mathematics, we analyse the downward Löwenheim-Skolem (DLS) theorem of first-order logic, stating that every infinite model has a countable elementary submodel. Refining the well-known equivalence of the DLS theorem
Dominik Kirst, Haoyi Zeng
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Dilators and the reverse mathematics zoo
Journal of Mathematical LogicA predilator is a particularly uniform transformation of linear orders. We have a dilator when the transformation preserves well-foundedness. Over the theory $\mathsf{ACA}_0$ from reverse mathematics, any $\Pi^1_2$-formula is equivalent to the statement ...
Anton Freund
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Graph Coloring and Reverse Mathematics
MLQ, 2000The author proves that for any natural numbers \(k\) and \(m\) such that \(2 \leq k \leq m\), \(\text{RCA}_0\) proves that \(\text{WKL}_0\) is equivalent to the statement ``if every finite subset of a graph can be \(k\)-colored, then the entire graph can be \(m\)-colored.'' Here, \(\text{RCA}_0\) and \(\text{WKL}_0\) are subsystems of arithmetic used ...
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On the reverse mathematics and Weihrauch complexity of moduli of regularity and uniqueness
De Computis, 2018The notion of ‘modulus of regularity’, as recently studied in [Moduli of regularity and rates of convergence for Fejér monotone sequences, 2017, Preprint], unifies a number of different concepts used in convex optimization to establish rates of ...
U. Kohlenbach
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Some Nonstandard Equivalences in Reverse Mathematics
Conference on Computability in Europe, 2018Reverse Mathematics (RM) is a program in the foundations of mathematics founded by Friedman and developed extensively by Simpson. The aim of RM is finding the minimal axioms needed to prove a theorem of ordinary (i.e. non-set theoretical) mathematics. In
Sam Sanders
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REVERSE MATHEMATICS OF MF SPACES
Journal of Mathematical Logic, 2006This paper gives a formalization of general topology in second-order arithmetic using countably based MF spaces. This formalization is used to study the reverse mathematics of general topology. For each poset P we let MF (P) denote the set of maximal filters on P endowed with the topology generated by {Np | p ∈ P}, where Np = {F ∈ MF (P) | p ∈ F}. We
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Reverse mathematics and semisimple rings
Archive for Mathematical Logic, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Splittings and Disjunctions in Reverse Mathematics
Notre Dame Journal of Formal Logic, 2020Sam Sanders
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Reverse Mathematics of Topology: Dimension, Paracompactness, and Splittings
Notre Dame Journal of Formal Logic, 2020Sam Sanders
exaly