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On the strength of a weak variant of the axiom of counting
Author(s) -
McKenzie Zachiri
Publication year - 2017
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201600004
Subject(s) - axiom of choice , mathematics , zermelo–fraenkel set theory , constructive set theory , urelement , consistency (knowledge bases) , axiom , axiom independence , set (abstract data type) , choice function , simple (philosophy) , function (biology) , infinity , set theory , discrete mathematics , mathematical economics , pure mathematics , computer science , mathematical analysis , epistemology , geometry , programming language , philosophy , evolutionary biology , biology
In this paper NFU − ACis used to denote Jensen's modification of Quine's ‘new foundations’ set theory ( NF ) fortified with a type‐level pairing function but without the axiom of choice. The axiom AxCount ≥ is the variant of the axiom of counting which asserts that no finite set is smaller than its own set of singletons. This paper shows thatNFU − AC + AxCount ≥proves the consistency of the simple theory of types with infinity ( TSTI ). This result implies that NF + AxCount ≥proves that consistency of TSTI , and thatNFU − AC + AxCount ≥proves the consistency of NFU − AC .