Maria Emilia Maietti ; Samuele Maschio ; Michael Rathjen - A realizability semantics for inductive formal topologies, Church's Thesis and Axiom of Choice

lmcs:5518 - Logical Methods in Computer Science, May 27, 2021, Volume 17, Issue 2 - https://doi.org/10.23638/LMCS-17(2:21)2021
A realizability semantics for inductive formal topologies, Church's Thesis and Axiom of Choice

Authors: Maria Emilia Maietti ; Samuele Maschio ; Michael Rathjen

We present a Kleene realizability semantics for the intensional level of the Minimalist Foundation, for short mtt, extended with inductively generated formal topologies, Church's thesis and axiom of choice. This semantics is an extension of the one used to show consistency of the intensional level of the Minimalist Foundation with the axiom of choice and formal Church's thesis in previous work. A main novelty here is that such a semantics is formalized in a constructive theory represented by Aczel's constructive set theory CZF extended with the regular extension axiom.


Volume: Volume 17, Issue 2
Published on: May 27, 2021
Accepted on: January 27, 2021
Submitted on: May 29, 2019
Keywords: Mathematics - Logic


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