About: Constructive mathematics, Church's Thesis, and free choice sequences

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type	http://eprints.org/ontology/ConferenceItemEPrint http://eprints.org/ontology/EPrint Article Academic Article
seeAlso	HTML Summary of #88974 Constructive mathematics, Church's Thesis, and free choice sequences
sameAs	Constructive mathematics, Church's Thesis, and free choice sequences
http://eprints.org/ontology/hasAccepted	Constructive mathematics, Church's Thesis, and free choice sequences (PDF)
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Title	Constructive mathematics, Church's Thesis, and free choice sequences
described by	https://demo.openlinksw.com/about/id/entity/https/raw.githubusercontent.com/annajordanous/CO644Files/main/export_kar_RDFN3.n3
Date	2021-07-02
Creator	David A. Turner
status	peer reviewed published
Publisher	Springer
abstract	We see the defining properties of constructive mathematics as being the proof interpretation of the logical connectives and the definition of function as rule or method. We sketch the development of intuitionist type theory as an alternative to set theory. We note that the axiom of choice is constructively valid for types, but not for sets. We see the theory of types, in which proofs are directly algorithmic, as a more natural setting for constructive mathematics than set theories like IZF. Church’s thesis provides an objective definition of effective computability. It cannot be proved mathematically because it is a conjecture about what kinds of mechanisms are physically possible, for which we have scientific evidence but not proof. We consider the idea of free choice sequences and argue that they do not undermine Church’s Thesis.
Is Part Of	Financial Cryptography and Data Security https://kar.kent.ac.uk/id/repository
Subject	QA 21 History of mathematics QA 75 Electronic computers. Computer science QA 8 Philosophy of mathematics
list of authors	https://kar.kent.ac.uk/id/eprint/88974#authors
presented at	17th Conference on Computability in Europe, CiE 2021
is topic of	https://raw.githubusercontent.com/annajordanous/CO644Files/main/export_kar_RDFN3.n3
is primary topic of	HTML Summary of #88974 Constructive mathematics, Church's Thesis, and free choice sequences

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