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Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp011831cn26p
Title: ON THE EQUICONSISTENCY OF ZFC AND ETCS WITH REPLACEMENT
Authors: Morgan, Peyton Keith
Advisors: Halvorson, Hans
Contributors: Burgess, John
Department: Mathematics
Class Year: 2015
Abstract: Discussions of the elementary theory of the category of sets (ETCS) often take for granted its ’equivalence’ with a form of conventional axiomatic set theory. The persuasiveness of such evocations of ’equivalence’ are complicated by their frequent omission of an axiom schema of replacement, even as their attendant expositions claim that the inclusion of replacement is generally unproblematic. Few sources test this assertion. In this expository paper, we articulate an axiom schema of replacement, R, within a categorical setting and prove the equiconsistency of ETCS + R and ZFC.
Extent: 22 pages
URI: http://arks.princeton.edu/ark:/88435/dsp011831cn26p
Type of Material: Princeton University Senior Theses
Language: en_US
Appears in Collections:Mathematics, 1934-2016

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