The axiom of determinacy implies dependent choice in mice

Mathematical Logic Quarterly 65 (3):370-375 (2019)
  Copy   BIBTEX

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.

Other Versions

No versions found

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 103,486

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

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.
Long Borel hierarchies.Arnold W. Miller - 2008 - Mathematical Logic Quarterly 54 (3):307-322.
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.
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)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Sandra Eleonore Müller
Ludwig Maximilians Universität, München

Citations of this work

No citations found.

Add more citations

References found in this work

Descriptive Set Theory.Yiannis Nicholas Moschovakis - 1982 - Studia Logica 41 (4):429-430.
Deconstructing inner model theory.Ralf-Dieter Schindler, John Steel & Martin Zeman - 2002 - Journal of Symbolic Logic 67 (2):721-736.
The real core model and its scales.Daniel W. Cunningham - 1995 - Annals of Pure and Applied Logic 72 (3):213-289.

Add more references