Determinacy and Jónsson cardinals in L

, , &
Journal of Symbolic Logic 79 (4):1184-1198 (2014)
  Copy   BIBTEX

Abstract

Assume ZF + AD +V=L and letκ< Θ be an uncountable cardinal. We show thatκis Jónsson, and that if cof = ω thenκis Rowbottom. We also establish some other partition properties.

Categories

Keywords

Reprint years

DOI

10.1017/jsl.2014.49

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,423

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

More Jonsson Algebras.Saharon Shelah - 2003 - Archive for Mathematical Logic 42 (1):1-44.
On successors of Jónsson cardinals.J. Vickers & P. D. Welch - 2000 - Archive for Mathematical Logic 39 (6):465-473.
Jónsson cardinals, erdös cardinals, and the core model.W. J. Mitchell - 1999 - Journal of Symbolic Logic 64 (3):1065-1086.
Large Cardinals, Inner Models, and Determinacy: An Introductory Overview.P. D. Welch - 2015 - Notre Dame Journal of Formal Logic 56 (1):213-242.
Rowbottom cardinals and Jonsson cardinals are almost the same.E. M. Kleinberg - 1973 - Journal of Symbolic Logic 38 (3):423-427.
The consistency strength of projective absoluteness.Kai Hauser - 1995 - Annals of Pure and Applied Logic 74 (3):245-295.
Bounds on the Strength of Ordinal Definable Determinacy in Small Admissible Sets.Diego Rojas-Rebolledo - 2012 - Notre Dame Journal of Formal Logic 53 (3):351-371.
A Cardinal Pattern Inspired by AD.Arthur W. Apter - 1996 - Mathematical Logic Quarterly 42 (1):211-218.
The largest countable inductive set is a mouse set.Mitch Rudominer - 1999 - Journal of Symbolic Logic 64 (2):443-459.
Successors of singular cardinals and coloring theorems I.Todd Eisworth & Saharon Shelah - 2005 - Archive for Mathematical Logic 44 (5):597-618.
Identity crises and strong compactness III: Woodin cardinals. [REVIEW]Arthur W. Apter & Grigor Sargsyan - 2006 - Archive for Mathematical Logic 45 (3):307-322.
No jónsson filters over ℵω.Jan Tryba - 1987 - Journal of Symbolic Logic 52 (1):51 - 53.
Review: Donald A. Martin, John R. Steel, Projective Determinacy; W. Hugh Woodin, Supercompact Cardinals, Sets of Reals, and Weakly Homogeneous Trees; Donald A. Martin, John R. Steel, A Proof of Projective Determinacy. [REVIEW]Matthew D. Foreman - 1992 - Journal of Symbolic Logic 57 (3):1132-1136.
Determinacy for Games Ending at the First Admissible Relative to the Play.Itay Neeman - 2006 - Journal of Symbolic Logic 71 (2):425 - 459.
No Jonsson Filters Over $aleph_omega$.Jan Tryba - 1987 - Journal of Symbolic Logic 52 (1):51-53.

Analytics

Added to PP
2016-06-30

Downloads
26 (#596,950)

6 months
8 (#347,798)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

W. Hugh Woodin
Harvard University

Citations of this work

Ordinal definability and combinatorics of equivalence relations.William Chan - 2019 - Journal of Mathematical Logic 19 (2):1950009.
A premouse inheriting strong cardinals from V.Farmer Schlutzenberg - 2020 - Annals of Pure and Applied Logic 171 (9):102826.

Add more citations

References found in this work

HOD L(ℝ) is a Core Model Below Θ.John R. Steel - 1995 - Bulletin of Symbolic Logic 1 (1):75-84.
HOD L(ℝ) is a Core Model Below Θ.John R. Steel - 1995 - Bulletin of Symbolic Logic 1 (1):75-84.

Add more references