2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/231472We 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).submitted; this is a revised version of an unsubmitted July 2003 preprint, now with a minimally improved upper boundLogic03E45 03F45 03E60 03E15text