David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 64 (2):407-435 (1999)
Aczel's theory of hypersets provides an interesting alternative to the standard view of sets as inductively constructed, well-founded objects, thus providing a convienent formalism in which to consider non-well-founded versions of classically well-founded constructions, such as the "circular logic" of . This theory and ZFC are mutually interpretable; in particular, any model of ZFC has a canonical "extension" to a non-well-founded universe. The construction of this model does not immediately generalize to weaker set theories such as the theory of admissible sets. In this paper, we formulate a version of Aczel's antifoundation axiom suitable for the theory of admissible sets. We investigate the properties of models of the axiom system KPU - , that is, KPU with foundation replaced by an appropriate strengthening of the extensionality axiom. Finally, we forge connections between "non-wellfounded sets over the admissible set A" and the fragment L A of the modal language L ∞
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Gerhard Jäger (1986). Theories for Admissible Sets: A Unifying Approach to Proof Theory. Bibliopolis.
Jon Barwise (1975). Admissible Sets and Structures: An Approach to Definability Theory. Springer-Verlag.
Ignacio Jané & Gabriel Uzquiano (2004). Well- and Non-Well-Founded Fregean Extensions. Journal of Philosophical Logic 33 (5):437-465.
Ingrid Lindström (1989). A Construction of Non-Well-Founded Sets Within Martin-Löf's Type Theory. Journal of Symbolic Logic 54 (1):57-64.
Jeremy Avigad (2002). An Ordinal Analysis of Admissible Set Theory Using Recursion on Ordinal Notations. Journal of Mathematical Logic 2 (1):91-112.
T. A. Slaman (1986). ∑1 Definitions with Parameters. Journal of Symbolic Logic 51 (2):453 - 461.
Mark Nadel & Jonathan Stavi (1977). The Pure Part of HYP(M). Journal of Symbolic Logic 42 (1):33-46.
Adam Rieger (2000). An Argument for Finsler-Aczel Set Theory. Mind 109 (434):241-253.
Sy D. Friedman (1979). HC of an Admissible Set. Journal of Symbolic Logic 44 (1):95-102.
Mujdat Pakkan & Varol Akman (1995). Hypersolver: A Graphical Tool for Commonsense Set Theory. Philosophical Explorations.
Added to index2009-01-28
Total downloads22 ( #173,117 of 1,907,930 )
Recent downloads (6 months)10 ( #66,304 of 1,907,930 )
How can I increase my downloads?