Philosophia Mathematica 24 (1):nku005 (2016)

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 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 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
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DOI 10.1093/philmat/nku005
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Frege's Cardinals and Neo-Logicism.Roy T. Cook - 2016 - Philosophia Mathematica 24 (1):60-90.
Paolo Mancosu.*Abstraction and Infinity. [REVIEW]Roy T. Cook & Michael Calasso - 2019 - Philosophia Mathematica 27 (1):125-152.

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