- New
-
Topics
- All Categories
- Metaphysics and Epistemology
- Value Theory
- Science, Logic, and Mathematics
- Science, Logic, and Mathematics
- Logic and Philosophy of Logic
- Philosophy of Biology
- Philosophy of Cognitive Science
- Philosophy of Computing and Information
- Philosophy of Mathematics
- Philosophy of Physical Science
- Philosophy of Social Science
- Philosophy of Probability
- General Philosophy of Science
- Philosophy of Science, Misc
- History of Western Philosophy
- Philosophical Traditions
- Philosophy, Misc
- Other Academic Areas
- Journals
- Submit material
- More
On the Consistency of a Positive Theory
Mathematical Logic Quarterly 45 (1):105-116 (1999)
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 cardinalsMy notes
Similar books and articles
An Interpretation of the Zermelo‐Fraenkel Set Theory and the Kelley‐Morse Set Theory in a Positive Theory.Olivier Esser - 1997 - Mathematical Logic Quarterly 43 (3):369-377.
Inconsistency of the Axiom of Choice with the Positive Theory $GPK^+ \infty$.Olivier Esser - 2000 - Journal of Symbolic Logic 65 (4):1911-1916.
Kelley-Morse+Types of well order is not a conservative extension of Kelley Morse.Haim Judah & M. Victoria Marshall - 1994 - Archive for Mathematical Logic 33 (1):13-21.
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.
An axiomatization of 'very' within systiems of set theory.Athanassios Tzouvaras - 2003 - Studia Logica 73 (3):413 - 430.
Analytics
Added to PP
2013-11-03
Downloads
2 (#1,450,151)
6 months
34 (#455,253)
2013-11-03
Downloads
2 (#1,450,151)
6 months
34 (#455,253)
Historical graph of downloads
Citations of this work
The Divine Fractal: 1st Order Extensional Theology.Paul Studtmann - 2021 - Philosophia 50 (1):285-305.
A Disquotational Theory of Truth as Strong as Z 2 −.Thomas Schindler - 2015 - Journal of Philosophical Logic 44 (4):395-410.
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.
An Interpretation of the Zermelo‐Fraenkel Set Theory and the Kelley‐Morse Set Theory in a Positive Theory.Olivier Esser - 1997 - Mathematical Logic Quarterly 43 (3):369-377.
PhilPapers logo by Andrea Andrews and Meghan Driscoll.
This site uses cookies and Google Analytics (see our terms & conditions for details regarding the privacy implications). Use of this site is subject to terms & conditions.
All rights reserved by The PhilPapers Foundation
Server: philpapers-web-68866f4b87-grz79 uwo