Well- and non-well-founded Fregean extensions

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

Authors
Gabriel Uzquiano
University of Southern California
Abstract
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.
Keywords AFA  Axiom V  extensions  George Boolos  Gottlob Frege  New V  non-well-founded sets  second-order set theory  ZFC
Categories (categorize this paper)
DOI 10.1023/B:LOGI.0000046129.22633.96
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 39,966
Through your library

References found in this work BETA

Iteration Again.George Boolos - 1989 - Philosophical Topics 17 (2):5-21.

Add more references

Citations of this work BETA

Relative Categoricity and Abstraction Principles.Sean Walsh & Sean Ebels-Duggan - 2015 - Review of Symbolic Logic 8 (3):572-606.
Bad Company Generalized.Gabriel Uzquiano - 2009 - Synthese 170 (3):331 - 347.

Add more citations

Similar books and articles

On Generic Extensions Without the Axiom of Choice.G. P. Monro - 1983 - Journal of Symbolic Logic 48 (1):39-52.
Conceptions and Paradoxes of Sets.G. Aldo Antonelli - 1999 - Philosophia Mathematica 7 (2):136-163.
Categoricity Theorems and Conceptions of Set.Gabriel Uzquiano - 2002 - Journal of Philosophical Logic 31 (2):181-196.
Blunt and Topless End Extensions of Models of Set Theory.Matt Kaufmann - 1983 - Journal of Symbolic Logic 48 (4):1053-1073.
Anti-Admissible Sets.Jacob Lurie - 1999 - Journal of Symbolic Logic 64 (2):407-435.

Analytics

Added to PP index
2009-01-28

Total views
108 ( #67,148 of 2,235,935 )

Recent downloads (6 months)
14 ( #58,109 of 2,235,935 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature