On the strength of a weak variant of the axiom of counting
McKenzie, Zachiri
McKenzie, Zachiri
Advisors
Editors
Other Contributors
Affiliation
EPub Date
Publication Date
2017-03-24
Submitted Date
Collections
Other Titles
Abstract
In this paper NFU-AC is 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 that NFU-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 that NFU-AC + AxCount>_ proves the consistency of NFU-AC.
Citation
McKenzie, Z. (2017). On the strength of a weak variant of the axiom of counting. Mathematical Logic Quarterly, 63(1-2), 94-103. https://doi.org/10.1002/malq.201600004
Publisher
Wiley
Wiley-VCH Verlag
Wiley-VCH Verlag
Journal
Mathematical Logic Quarterly
Research Unit
DOI
10.1002/malq.201600004
PubMed ID
PubMed Central ID
Type
Article
Language
en
Description
This article is not available on ChesterRep
Series/Report no.
ISSN
0942-5616
EISSN
1521-3870
ISBN
ISMN
Gov't Doc
Test Link
Sponsors
Unfunded