Δ 0 3 -determinacy, comprehension and induction

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Journal of Symbolic Logic 72 (2):452-462 (2007)
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Abstract

We show that each of Δ13-CA0 + Σ13-IND and Π12-CA0 + Π13-TI proves Δ03-Det and that neither Σ31-IND nor Π13-TI can be dropped. We also show that neither Δ13-CA0 + Σ1∞-IND nor Π12-CA0 + Π1∞-TI proves Σ03-Det. Moreover, we prove that none of Δ21-CA0, Σ31-IND and Π21-TI is provable in Δ11-Det0 = ACA0 + Δ11-Det

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10.2178/jsl/1185803618

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Citations of this work

Open questions in reverse mathematics.Antonio Montalbán - 2011 - Bulletin of Symbolic Logic 17 (3):431-454.
Games for truth.P. D. Welch - 2009 - Bulletin of Symbolic Logic 15 (4):410-427.
Reverse mathematics: the playground of logic.Richard A. Shore - 2010 - Bulletin of Symbolic Logic 16 (3):378-402.

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References found in this work

Weak axioms of determinacy and subsystems of analysis II.Kazuyuki Tanaka - 1991 - Annals of Pure and Applied Logic 52 (1-2):181-193.
Weak axioms of determinacy and subsystems of analysis I: δ20 games.Kazuyuki Tanaka - 1990 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 36 (6):481-491.
Bar induction and ω model reflection.Gerhard Jäger & Thomas Strahm - 1999 - Annals of Pure and Applied Logic 97 (1-3):221-230.
Higher set theory and mathematical practice.Harvey M. Friedman - 1971 - Annals of Mathematical Logic 2 (3):325.

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