Mice with finitely many Woodin cardinals from optimal determinacy hypotheses
Journal of Mathematical Logic 20 (Supp01):1950013 (2020)
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.Author Profiles
DOI
10.1142/s0219061319500132
My notes
Similar books and articles
Ordinal definability and combinatorics of equivalence relations.William Chan - 2019 - Journal of Mathematical Logic 19 (2):1950009.
Collapsing the cardinals of HOD.James Cummings, Sy David Friedman & Mohammad Golshani - 2015 - Journal of Mathematical Logic 15 (2):1550007.
On cuts in ultraproducts of linear orders I.Mohammad Golshani & Saharon Shelah - 2016 - Journal of Mathematical Logic 16 (2):1650008.
Locally definable subgroups of semialgebraic groups.Elías Baro, Pantelis E. Eleftheriou & Ya’Acov Peterzil - 2019 - Journal of Mathematical Logic 20 (2):2050009.
The Bristol model: An abyss called a Cohen real.Asaf Karagila - 2018 - Journal of Mathematical Logic 18 (2):1850008.
Specializing trees and answer to a question of Williams.Mohammad Golshani & Saharon Shelah - 2020 - Journal of Mathematical Logic 21 (1):2050023.
Categoricity from one successor cardinal in Tame abstract elementary classes.Rami Grossberg & Monica Vandieren - 2006 - Journal of Mathematical Logic 6 (2):181-201.
Galois-stability for Tame abstract elementary classes.Rami Grossberg & Monica Vandieren - 2006 - Journal of Mathematical Logic 6 (01):25-48.
On the definability of the double jump in the computably enumerable sets.Peter A. Cholak & Leo A. Harrington - 2002 - Journal of Mathematical Logic 2 (02):261-296.
Bounds on Scott ranks of some polish metric spaces.William Chan - 2020 - Journal of Mathematical Logic 21 (1):2150001.
Independence in randomizations.Uri Andrews, Isaac Goldbring & H. Jerome Keisler - 2019 - Journal of Mathematical Logic 19 (1):1950005.
Polynomial local search in the polynomial hierarchy and witnessing in fragments of bounded arithmetic.Arnold Beckmann & Samuel R. Buss - 2009 - Journal of Mathematical Logic 9 (1):103-138.
Definable V-topologies, Henselianity and NIP.Yatir Halevi, Assaf Hasson & Franziska Jahnke - 2019 - Journal of Mathematical Logic 20 (2):2050008.
Analytics
Added to PP
2020-07-28
Downloads
19 (#589,775)
6 months
2 (#300,644)
2020-07-28
Downloads
19 (#589,775)
6 months
2 (#300,644)
Historical graph of downloads
Author Profiles
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.
Projective Games on the Reals.Juan P. Aguilera & Sandra Müller - 2020 - Notre Dame Journal of Formal Logic 61 (4):573-589.
In inner models with Woodin cardinals.Sandra Müller & Grigor Sargsyan - 2021 - Journal of Symbolic Logic 86 (3):871-896.
Constructing wadge classes.Raphaël Carroy, Andrea Medini & Sandra Müller - 2022 - Bulletin of Symbolic Logic 28 (2):207-257.
Forcing the [math]-separation property.Stefan Hoffelner - 2022 - Journal of Mathematical Logic 22 (2).
References found in this work
Analytic determinacy and 0#. [REVIEW]Leo Harrington - 1978 - Journal of Symbolic Logic 43 (4):685 - 693.
The fine structure of the constructible hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.
Inner models with many Woodin cardinals.J. R. Steel - 1993 - Annals of Pure and Applied Logic 65 (2):185-209.