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The Combinatorics of Non-well-founded Sets

In: Finsler Set Theory: Platonism and Circularity

Author

Listed:
  • David Booth

    (Three Fold Foundation 307)

  • Renatus Ziegler

    (Mathematisch-Astronomische Sektion am Geotheanum)

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.

Suggested Citation

  • David Booth & Renatus Ziegler, 1996. "The Combinatorics of Non-well-founded Sets," Springer Books, in: David Booth & Renatus Ziegler (ed.), Finsler Set Theory: Platonism and Circularity, pages 215-240, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-9031-1_16
    DOI: 10.1007/978-3-0348-9031-1_16
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