The weak choice principle WISC may fail in the category of sets

dc.contributor.author	Roberts, D.
dc.date.issued	2015
dc.description.abstract	The set-theoretic axiom WISC states that for every set there is a set of surjections to it cofinal in all such surjections. By constructing an unbounded topos over the category of sets and using an extension of the internal logic of a topos due to Shulman, we show that WISC is independent of the rest of the axioms of the set theory given by a well-pointed topos. This also gives an example of a topos that is not a predicative topos as defined by van den Berg.
dc.description.statementofresponsibility	David Michael Roberts
dc.identifier.citation	Studia Logica, 2015; 103(5):1005-1017
dc.identifier.doi	10.1007/s11225-015-9603-6
dc.identifier.issn	0039-3215
dc.identifier.issn	1572-8730
dc.identifier.orcid	Roberts, D. [0000-0002-3478-0522]
dc.identifier.uri	http://hdl.handle.net/2440/102117
dc.language.iso	en
dc.publisher	Kluwer Academic Publishers
dc.relation.grant	http://purl.org/au-research/grants/arc/DP120100106
dc.rights	© Springer Science+Business Media Dordrecht 2015
dc.source.uri	https://doi.org/10.1007/s11225-015-9603-6
dc.subject	Choice principle
dc.subject	ETCS
dc.subject	Set theory
dc.subject	Toposes
dc.subject	WISC
dc.title	The weak choice principle WISC may fail in the category of sets
dc.type	Journal article
pubs.publication-status	Published

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