Mice with finitely many Woodin cardinals from optimal determinacy hypotheses

, &
Journal of Mathematical Logic 20 (Supp01):1950013 (2020)
  Copy   BIBTEX

Abstract

We prove the following result which is due to the third author. Let [Formula: see text]. If [Formula: see text] determinacy and [Formula: see text] determinacy both hold true and there is no [Formula: see text]-definable [Formula: see text]-sequence of pairwise distinct reals, then [Formula: see text] exists and is [Formula: see text]-iterable. The proof yields that [Formula: see text] determinacy implies that [Formula: see text] exists and is [Formula: see text]-iterable for all reals [Formula: see text]. A consequence is the Determinacy Transfer Theorem for arbitrary [Formula: see text], namely the statement that [Formula: see text] determinacy implies [Formula: see text] determinacy.

Categories

Keywords

Reprint years

DOI

10.1142/s0219061319500132

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,219

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

Pure and Hybrid Mice with Finitely Many Woodin Cardinals from Levels of Determinacy Westfälische Wilhelms-Universität Münster, Germany, 2016. Supervised by Ralf-Dieter Schindler.Sandra Müller - 2018 - Bulletin of Symbolic Logic 24 (2):198-198.
Core Models in the Presence of Woodin Cardinals.Ralf Schindler - 2006 - Journal of Symbolic Logic 71 (4):1145 - 1154.
Inner models in the region of a Woodin limit of Woodin cardinals.Itay Neeman - 2002 - Annals of Pure and Applied Logic 116 (1-3):67-155.
The consistency strength of projective absoluteness.Kai Hauser - 1995 - Annals of Pure and Applied Logic 74 (3):245-295.
Identity crises and strong compactness III: Woodin cardinals. [REVIEW]Arthur W. Apter & Grigor Sargsyan - 2006 - Archive for Mathematical Logic 45 (3):307-322.
Stacking mice.Ronald Jensen, Ernest Schimmerling, Ralf Schindler & John Steel - 2009 - Journal of Symbolic Logic 74 (1):315-335.
The largest countable inductive set is a mouse set.Mitch Rudominer - 1999 - Journal of Symbolic Logic 64 (2):443-459.
Easton’s theorem in the presence of Woodin cardinals.Brent Cody - 2013 - Archive for Mathematical Logic 52 (5-6):569-591.
Determinacy for Games Ending at the First Admissible Relative to the Play.Itay Neeman - 2006 - Journal of Symbolic Logic 71 (2):425 - 459.
Inner model operators in L.Mitch Rudominer - 2000 - Annals of Pure and Applied Logic 101 (2-3):147-184.
Determinacy and Jónsson cardinals in L.S. Jackson, R. Ketchersid, F. Schlutzenberg & W. H. Woodin - 2014 - Journal of Symbolic Logic 79 (4):1184-1198.
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.
On a problem of Woodin.Arthur W. Apter - 2000 - Archive for Mathematical Logic 39 (4):253-259.
Elementary chains and C (n)-cardinals.Konstantinos Tsaprounis - 2014 - Archive for Mathematical Logic 53 (1-2):89-118.
The HOD Hypothesis and a supercompact cardinal.Yong Cheng - 2017 - Mathematical Logic Quarterly 63 (5):462-472.

Analytics

Added to PP
2019-06-07

Downloads
30 (#504,503)

6 months
9 (#250,037)

Historical graph of downloads
How can I increase my downloads?

Author Profiles

Ralf Schindler
W. Hugh Woodin
Harvard University
Sandra Eleonore Müller
Ludwig Maximilians Universität, München

Citations of this work

Long games and σ-projective sets.Juan P. Aguilera, Sandra Müller & Philipp Schlicht - 2021 - Annals of Pure and Applied Logic 172 (4):102939.
Forcing the [math]-separation property.Stefan Hoffelner - 2022 - Journal of Mathematical Logic 22 (2).
Constructing wadge classes.Raphaël Carroy, Andrea Medini & Sandra Müller - 2022 - Bulletin of Symbolic Logic 28 (2):207-257.
Projective Games on the Reals.Juan P. Aguilera & Sandra Müller - 2020 - Notre Dame Journal of Formal Logic 61 (4):573-589.

View all 6 citations / Add more citations

References found in this work

The Higher Infinite.Akihiro Kanamori - 2000 - Studia Logica 65 (3):443-446.
Set Theory.Thomas Jech - 1999 - Studia Logica 63 (2):300-300.
Inner models with many Woodin cardinals.J. R. Steel - 1993 - Annals of Pure and Applied Logic 65 (2):185-209.
$K$ without the measurable.Ronald Jensen & John Steel - 2013 - Journal of Symbolic Logic 78 (3):708-734.
The fine structure of the constructible hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.

View all 16 references / Add more references