The Combinatorics of Non-well-founded Sets

David Booth and Renatus Ziegler
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David Booth: Three Fold Foundation 307
Renatus Ziegler: Mathematisch-Astronomische Sektion am Geotheanum

A chapter in Finsler Set Theory: Platonism and Circularity, 1996, pp 215-240 from Springer

Abstract: Abstract Even though non-well-founded sets appeared in Mirimanoff [1917a] the most significant early treatment was that of Finsler [1926b]. Since then there have been studies of set theory without an axiom of foundation, but these have usually been relative consistency arguments that fell short of accepting non-well-founded sets themselves. The publication of Aczel [1988] marked a change in this respect: Aczel gave an anti-foundation axiom that replace the axiom of foundation. He also compared Finsler’s axiom of identity to his anti-foundation axiom.

Keywords: Transitive Closure; Ordinal Number; Binomial Coefficient; Fibonacci Sequence; Isomorphism Type (search for similar items in EconPapers)
Date: 1996
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DOI: 10.1007/978-3-0348-9031-1_16

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