The Axiom of Regularity

  • Vaught R
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Abstract

"The axiom of regularity" (reg) says that all sets are regular (i.e., well-founded). set theory is a language for representing (intuitive) mathematical relations. i show that 'reg' is true in the sense that we can assume it without loss of generality; i.e., i show that any relation that can be represented by a set can already be represented by a regular set. nevertheless, i argue for the need for logicians to study sets in general in order to explicate the concept of a set. and to this end i present many results bearing on non-regular sets.

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APA

Vaught, R. L. (2001). The Axiom of Regularity. In Set Theory (pp. 91–98). Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-0835-8_9

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