Well- and non-well-founded Fregean extensions

Journal of Philosophical Logic 33 (5):437-465 (2004)
  Copy   BIBTEX


George Boolos has described an interpretation of a fragment of ZFC in a consistent second-order theory whose only axiom is a modification of Frege's inconsistent Axiom V. We build on Boolos's interpretation and study the models of a variety of such theories obtained by amending Axiom V in the spirit of a limitation of size principle. After providing a complete structural description of all well-founded models, we turn to the non-well-founded ones. We show how to build models in which foundation fails in prescribed ways. In particular, we obtain models in which every relation is isomorphic to the membership relation on some set as well as models of Aczel's anti-foundation axiom (AFA). We suggest that Fregean extensions provide a natural way to envisage non-well-founded membership.



    Upload a copy of this work     Papers currently archived: 84,049

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Blunt and topless end extensions of models of set theory.Matt Kaufmann - 1983 - Journal of Symbolic Logic 48 (4):1053-1073.
Categoricity theorems and conceptions of set.Gabriel Uzquiano - 2002 - Journal of Philosophical Logic 31 (2):181-196.
Conceptions and paradoxes of sets.G. Aldo Antonelli - 1999 - Philosophia Mathematica 7 (2):136-163.
On generic extensions without the axiom of choice.G. P. Monro - 1983 - Journal of Symbolic Logic 48 (1):39-52.
Anti-admissible sets.Jacob Lurie - 1999 - Journal of Symbolic Logic 64 (2):407-435.


Added to PP

143 (#103,527)

6 months
3 (#248,477)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Gabriel Uzquiano
University of Southern California

Citations of this work

Relative categoricity and abstraction principles.Sean Walsh & Sean Ebels-Duggan - 2015 - Review of Symbolic Logic 8 (3):572-606.
Iteration one more time.Roy T. Cook - 2003 - Notre Dame Journal of Formal Logic 44 (2):63--92.
Bad company generalized.Gabriel Uzquiano - 2009 - Synthese 170 (3):331 - 347.
Identifying finite cardinal abstracts.Sean C. Ebels-Duggan - 2020 - Philosophical Studies 178 (5):1603-1630.

View all 8 citations / Add more citations

References found in this work

Iteration Again.George Boolos - 1989 - Philosophical Topics 17 (2):5-21.
Non-Well-Founded Sets.Peter Aczel - 1988 - Palo Alto, CA, USA: Csli Lecture Notes.

View all 7 references / Add more references