200 research outputs found
Natural density and probability, constructively
No full textWe give a constructive account of the frequentist approach to probability, by means of natural density. Then we discuss some probabilistic variants of the Limited Principle of Omniscience
Implicative models of set theory
No full textIn this paper we show that using implicative algebras one can produce modelsof set theory generalizing Heyting/Boolean-valued models and realizabilitymodels of (I)ZF, both in intuitionistic and classical logic. This has asconsequence that any topos which is obtained from a Set-based tripos as theresult of the tripos-to-topos construction hosts a model of intuitionistic orclassical set theory, provided a large enough strongly inaccessible cardinalexists.Comment: arXiv admin note: substantial text overlap with arXiv:2301.1174
A realizability semantics for inductive formal topologies, church’s thesis and axiom of choice
No full textWe present a Kleene realizability semantics for the intensional level of the Minimalist Foundation, for short mTT, extended with inductively generated formal topologies, the formal Church’s thesis and axiom of choice. This semantics is an extension of the one used to show the consistency of the intensional level of the Minimalist Foundation with the axiom of choice and the formal Church’s thesis in the work by Ishihara, Maietti, Maschio, Streicher [Arch.Math.Logic,57(7-8):873-888,2018]. A main novelty here is that such a semantics is formalized in a constructive theory as Aczel’s constructive set theory CZF extended with the regular extension axiom
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