Weak systems of determinacy and arithmetical quasi-inductive definitions

P. D. Welch

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arXiv · 0905.4412

Weak systems of determinacy and arithmetical quasi-inductive definitions

P. D. Welch

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Abstract

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).

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BibTeX RIS

P. D. Welch. 2009-05-26. Weak systems of determinacy and arithmetical quasi-inductive definitions. https://arxiv.org/abs/0905.4412

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