On the Consistency of a Positive Theory

Mathematical Logic Quarterly 45 (1):105-116 (1999)
  Copy   BIBTEX

Abstract

In positive theories, we have an axiom scheme of comprehension for positive formulas. We study here the “generalized positive” theory GPK∞+. Natural models of this theory are hyperuniverses. The author has shown in [2] that GPK∞+ interprets the Kelley Morse class theory. Here we prove that GPK∞+ + ACWF and the Kelley-Morse class theory with the axiom of global choice and the axiom “On is ramifiable” are mutually interpretable. This shows that GPK∞+ + ACWF is a “strong” theory since “On is ramifiable” implies the existence of a proper class of inaccessible cardinals

Other Versions

No versions found

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 99,462

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

Inconsistency of GPK + AFA.Olivier Esser - 1996 - Mathematical Logic Quarterly 42 (1):104-108.
Fixed-points of Set-continuous Operators.O. Esser, R. Hinnion & D. Dzierzgowski - 2000 - Mathematical Logic Quarterly 46 (2):183-194.
Positive abstraction and extensionality.Roland Hinnion & Thierry Libert - 2003 - Journal of Symbolic Logic 68 (3):828-836.
Hyperclass forcing in Morse-Kelley class theory.Carolin Antos & Sy-David Friedman - 2017 - Journal of Symbolic Logic 82 (2):549-575.
Types in class set theory and inaccessible cardinals.M. Victoria Marshall - 1996 - Archive for Mathematical Logic 35 (3):145-156.
Classes and truths in set theory.Kentaro Fujimoto - 2012 - Annals of Pure and Applied Logic 163 (11):1484-1523.

Analytics

Added to PP
2013-11-03

Downloads
40 (#455,475)

6 months
6 (#693,786)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

The iterative conception of set.Thomas Forster - 2008 - Review of Symbolic Logic 1 (1):97-110.
A Disquotational Theory of Truth as Strong as Z 2 −.Thomas Schindler - 2015 - Journal of Philosophical Logic 44 (4):395-410.
What is categorical structuralism?Geoffrey Hellman - 2006 - In Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics: Assessing Philosophy of Logic and Mathematics Today. Dordrecht, Netherland: Springer. pp. 151--161.
Type-free truth.Thomas Schindler - 2015 - Dissertation, Ludwig Maximilians Universität München

View all 13 citations / Add more citations

References found in this work

The consistency problem for positive comprehension principles.M. Forti & R. Hinnion - 1989 - Journal of Symbolic Logic 54 (4):1401-1418.
Choice principles in hyperuniverses.Marco Forti & Furio Honsell - 1996 - Annals of Pure and Applied Logic 77 (1):35-52.
Inconsistency of GPK + AFA.Olivier Esser - 1996 - Mathematical Logic Quarterly 42 (1):104-108.

Add more references