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References (18)
-
Andrew Marks (2018)
Set theoryMathematical Statistics with Applications in R
-
Sherwood Hachtman (2017)
CALIBRATING DETERMINACY STRENGTH IN LEVELS OF THE BOREL HIERARCHYThe Journal of Symbolic Logic, 82
-
T Jech (2003)
Set Theory. The Third Millennium Edition, Revised and Expanded -
A Montalbán, RA Shore (2012)
The limits of determinacy in second-order arithmeticProc. Lond. Math. Soc. (3), 104
-
J. Barwise (1976)
Admissible Sets and Structures: An Approach to Definability Theory -
(1977)
Determinateness and subsystems of analysis -
R Schindler, M Zeman (2010)
Handbook of Set Theory -
V Gitman, JD Hamkins (2017)
Foundations of Mathematics -
J Barwise (1975)
Admissible Sets and Structures: An Approach to Definability Theory, Perspectives in Mathematical Logic -
H. Hermes (1973)
Introduction to mathematical logic -
Sherwood Hachtman (2017)
Determinacy in third order arithmeticAnn. Pure Appl. Log., 168
-
G. Haeffler, U. Ljungblad, I. Kiyan, D. Hanstorp (1997)
Fine structure of As−Zeitschrift für Physik D Atoms, Molecules and Clusters, 42
-
R. Jensen (1972)
The fine structure of the constructible hierarchyAnnals of Mathematical Logic, 4
-
A. Montalbán, R. Shore (2012)
The limits of determinacy in second order arithmetic: consistency and complexity strengthIsrael Journal of Mathematics, 204
-
N. Schweber (2013)
TRANSFINITE RECURSION IN HIGHER REVERSE MATHEMATICSThe Journal of Symbolic Logic, 80
-
V. Gitman, J. Hamkins (2015)
Open determinacy for class gamesarXiv: Logic
-
H. Friedman (1971)
Higher set theory and mathematical practiceAnnals of Mathematical Logic, 2
-
Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations
- Publisher
- Springer Journals
- Copyright
- Copyright © 2019 by Springer-Verlag GmbH Germany, part of Springer Nature
- Subject
- Mathematics; Mathematical Logic and Foundations; Mathematics, general; Algebra
- ISSN
- 0933-5846
- eISSN
- 1432-0665
- DOI
- 10.1007/s00153-018-0655-y
- Publisher site
- See Article on Publisher Site
Abstract
We show, assuming weak large cardinals, that in the context of games of length $$\omega $$ ω with moves coming from a proper class, clopen determinacy is strictly weaker than open determinacy. The proof amounts to an analysis of a certain level of L that exists under large cardinal assumptions weaker than an inaccessible. Our argument is sufficiently general to give a family of determinacy separation results applying in any setting where the universal class is sufficiently closed; e.g., in third, seventh, or $$(\omega +2)$$ ( ω + 2 ) th order arithmetic. We also prove bounds on the strength of Borel determinacy for proper class games. These results answer questions of Gitman and Hamkins.
Journal
Archive for Mathematical Logic – Springer Journals
Published: Jan 2, 2019