- 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
The axiom of determinacy implies dependent choice in mice
Mathematical Logic Quarterly 65 (3):370-375 (2019)
Abstract
We show that the Axiom of Dependent Choice,, holds in countably iterable, passive premice constructed over their reals which satisfy the Axiom of Determinacy,, in a background universe. This generalizes an argument of Kechris for using Steel's analysis of scales in mice. In particular, we show that for any and any countable set of reals A so that and, we have that.Author's Profile
Other Versions
No versions found
My notes
Similar books and articles
Determinate logic and the Axiom of Choice.J. P. Aguilera - 2020 - Annals of Pure and Applied Logic 171 (2):102745.
Shadows of the axiom of choice in the universe $$L$$.Jan Mycielski & Grzegorz Tomkowicz - 2018 - Archive for Mathematical Logic 57 (5-6):607-616.
Disasters in topology without the axiom of choice.Kyriakos Keremedis - 2001 - Archive for Mathematical Logic 40 (8):569-580.
Does Imply, Uniformly?Alessandro Andretta & Lorenzo Notaro - forthcoming - Journal of Symbolic Logic:1-25.
The model of set theory generated by countably many generic reals.Andreas Blass - 1981 - Journal of Symbolic Logic 46 (4):732-752.
A parametrised choice principle and Martin's conjecture on Blackwell determinacy.Benedikt Löwe - 2006 - Mathematical Logic Quarterly 52 (2):187-189.
The consistency strength of long projective determinacy.Juan P. Aguilera & Sandra Müller - 2019 - Journal of Symbolic Logic 85 (1):338-366.
Preservation of choice principles under realizability.Eman Dihoum & Michael Rathjen - 2019 - Logic Journal of the IGPL 27 (5):746-765.
Analytics
Added to PP
2019-10-15
Downloads
21 (#1,064,256)
6 months
9 (#365,566)
2019-10-15
Downloads
21 (#1,064,256)
6 months
9 (#365,566)
Historical graph of downloads
Author's Profile
References found in this work
Deconstructing inner model theory.Ralf-Dieter Schindler, John Steel & Martin Zeman - 2002 - Journal of Symbolic Logic 67 (2):721-736.
The axiom of determinancy implies dependent choices in l(r).Alexander S. Kechris - 1984 - Journal of Symbolic Logic 49 (1):161 - 173.
The real core model and its scales.Daniel W. Cunningham - 1995 - Annals of Pure and Applied Logic 72 (3):213-289.
The consistency strength of long projective determinacy.Juan P. Aguilera & Sandra Müller - 2019 - Journal of Symbolic Logic 85 (1):338-366.
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-99fc7d78b-gv576 uwo