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Classical recursion theory
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Theories of Recursive functions, Hierarchies of recursive functions, and Arithmetical sets: Recursively enumerable sets.Abstract:
Preface. Introduction. Theories of Recursive functions. Hierarchies of recursive functions. Recursively enumerable sets. Recursively enumerable degrees. Limit sets. Arithmetical sets. Arithmetical degrees. Enumeration degrees. Bibliography. Notation index. Subject index.read more
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Realizability Semantics for Quantified Modal Logic : Generalizing Flagg's 1985 Construction
Benjamin G. Rin,Sean Walsh +1 more
TL;DR: In this article, a semantics for quantified modal logic is presented that is based on Kleene's notion of realizability, which generalizes Flagg's 1985 construction of a model of a modal version of Church's Thesis and first-order arithmetic.
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On Derivatives and Subpattern Orders of Countable Subshifts
Ville Salo,Ilkka Törmä +1 more
TL;DR: An SFT whose iterated derivatives are maximally complex from the computational point of view, a sofic shift whose sub pattern poset contains an infinite descending chain, a family of SFTs whose finite subpattern posets contain arbitrary finite posets, and a natural example of an SFT with infinite Cantor-Bendixon rank are presented.
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First-Order Logic in the Medvedev Lattice
TL;DR: This work extends the work of Medvedev to first-order logic, using the notion of a first- order hyperdoctrine from categorical logic, to a structure which is called the hyper doctrine of mass problems, and studies the intermediate logic and the theories of subintervals of this structure to obtain an analogue of Skvortsova's result.
Randomness in Physics: Five Questions, Some Answers
TL;DR: Despite provable unknowables in recursion theory, indeterminism and randomness in physics is confined to conventions, subjective beliefs and preliminary evidence as mentioned in this paper, and the history of the issue is very briefly reviewed, and answers to five questions raised by Zenil are
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Preface: 8th Conference on Real Numbers and Computers
Marc Daumas,Javier D. Bruguera +1 more
TL;DR: The lecture is a report on current research activities of the MuPAD group in the area of symbolic and numeric solutions of ODE (ordinary differential equations) based on a unification of Lie-point-symmetries and Lie-Bäcklund-sympetries, opening new avenues for using integrability for wider classes of differential equations.