The Decidability of the Class and the Axiom of Foundation

&
Notre Dame Journal of Formal Logic 42 (1):41-53 (2001)
  Copy   BIBTEX

Abstract

We show that the Axiom of Foundation, as well as the Antifoundation Axiom AFA, plays a crucial role in determining the decidability of the following problem. Given a first-order theory T over the language , and a sentence F of the form with quantifier-free in the same language, are there models of T in which F is true? Furthermore we show that the Extensionality Axiom is quite irrelevant in that respect

Categories

Keywords

Reprint years

DOI

10.1305/ndjfl/1054301354

Other Versions

original Bellè, Dorella; Parlamento, Franco (2001) "The Decidability of the $ \forall^*\exists$ Class and the Axiom of Foundation". Notre Dame Journal of Formal Logic 42(1):41-53

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 101,105

External links

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

Through your library

My notes

Similar books and articles

Decidability and Completeness for Open Formulas of Membership Theories.Dorella Bellè & Franco Parlamento - 1995 - Notre Dame Journal of Formal Logic 36 (2):304-318.
The decision problem for restricted universal quantification in set theory and the axiom of foundation.Franco Parlamento & Alberto Policriti - 1992 - Mathematical Logic Quarterly 38 (1):143-156.
Dependent Choices and Anti-Foundation.Hisato Muraki - 2002 - Mathematical Logic Quarterly 48 (4):607-623.
Well- and non-well-founded Fregean extensions.Ignacio Jané & Gabriel Uzquiano - 2004 - Journal of Philosophical Logic 33 (5):437-465.
Inconsistency of GPK + AFA.Olivier Esser - 1996 - Mathematical Logic Quarterly 42 (1):104-108.
EM + Ext_ + AC~i~n~t is equivalent to AC~e~x~t.Jesper Carlström - 2004 - Mathematical Logic Quarterly 50 (3):236.
Independence, randomness and the axiom of choice.Michiel van Lambalgen - 1992 - Journal of Symbolic Logic 57 (4):1274-1304.
The strength of extensionality I—weak weak set theories with infinity.Kentaro Sato - 2009 - Annals of Pure and Applied Logic 157 (2-3):234-268.
Kripke-Platek Set Theory and the Anti-Foundation Axiom.Michael Rathjen - 2001 - Mathematical Logic Quarterly 47 (4):435-440.

Analytics

Added to PP
2013-11-01

Downloads
40 (#540,060)

6 months
12 (#263,087)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references