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arXiv:0905.4412 [math.LO]AbstractReferencesReviewsResources

Weak systems of determinacy and arithmetical quasi-inductive definitions

P. D. Welch

Published 2009-05-26Version 1

We locate winning strategies for various Sigma^0_3-games in the L-hierarchy in order to prove that Sigma^0_3 Determinacy is intermediate between Pi^1_3-CA_0 (even Pi^1_2-CA_0 (lightface) with Pi^1_3-lightface definable parameters allowed) and Delta^1_3-CA_0 + AQI. (Here "AQI" is the statement in second order number theory that every arithmeical quasi-inductive definition on any input stabilizes).

Comments: submitted; this is a revised version of an unsubmitted July 2003 preprint, now with a minimally improved upper bound
Categories: math.LO
Subjects: 03E45, 03F45, 03E60, 03E15
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