Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/102117
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Type: | Journal article |
Title: | The weak choice principle WISC may fail in the category of sets |
Author: | Roberts, D. |
Citation: | Studia Logica: an international journal for symbolic logic, 2015; 103(5):1005-1017 |
Publisher: | Kluwer Academic Publishers |
Issue Date: | 2015 |
ISSN: | 0039-3215 1572-8730 |
Statement of Responsibility: | David Michael Roberts |
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. |
Keywords: | Choice principle ETCS Set theory Toposes WISC |
Rights: | © Springer Science+Business Media Dordrecht 2015 |
DOI: | 10.1007/s11225-015-9603-6 |
Grant ID: | http://purl.org/au-research/grants/arc/DP120100106 |
Published version: | http://dx.doi.org/10.1007/s11225-015-9603-6 |
Appears in Collections: | Aurora harvest 3 Mathematical Sciences publications |
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hdl_102117.pdf | Accepted version | 583.79 kB | Adobe PDF | View/Open |
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