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- Title
Mathematical Objects arising from Equivalence Relations and their Implementation in Quine's NF.
- Authors
Forster, Thomas
- Abstract
Many mathematical objects arise from equivalence classes and invite implementation as those classes. Set-existence principles that would enable this are incompatible with ZFC's unrestricted aussonderung but there are set theories (e.g., NF and Church's CUS) which admit more instances than does ZF. NF provides equivalence classes for stratified relations only. Church's construction provides equivalence classes for "low" sets, and thus, for example, a set of all (low) ordinals. However, that set has an ordinal in turn which is not a member of the set constructed; so no set of all ordinals is obtained thereby. This "recurrence problem" is discussed.
- Subjects
MATHEMATICAL ability; MATHEMATICAL equivalence; SET theory; ORDINALS (Liturgical books); CARDINAL numbers
- Publication
Philosophia Mathematica, 2016, Vol 24, Issue 1, p50
- ISSN
0031-8019
- Publication type
Article
- DOI
10.1093/philmat/nku005