Maietti, Maria Emilia and Pasquali, Fabio and Rosolini, Giuseppe - Elementary Quotient Completions, Church's Thesis, and Partioned Assemblies

lmcs:4302 - Logical Methods in Computer Science, June 25, 2019, Volume 15, Issue 2
Elementary Quotient Completions, Church's Thesis, and Partioned Assemblies

Authors: Maietti, Maria Emilia and Pasquali, Fabio and Rosolini, Giuseppe

Hyland's effective topos offers an important realizability model for constructive mathematics in the form of a category whose internal logic validates Church's Thesis. It also contains a boolean full sub-quasitopos of "assemblies" where only a restricted form of Church's Thesis survives. In the present paper we compare the effective topos and the quasitopos of assemblies each as the elementary quotient completions of a Lawvere doctrine based on the partitioned assemblies. In that way we can explain why the two forms of Church's Thesis each category satisfies differ by the way each is inherited from specific properties of the doctrine which determines the elementary quotient completion.


Source : oai:arXiv.org:1802.06400
DOI : 10.23638/LMCS-15(2:21)2019
Volume: Volume 15, Issue 2
Published on: June 25, 2019
Submitted on: February 20, 2018
Keywords: Mathematics - Logic


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