以下の要領でコロキウムを開催します．
日時：2013年2月18日（月）15:10-16:40 場所：神戸大学自然科学総合研究棟3号館4階421室（プレゼンテーション室） 講演者：Philip Welch (Univ. of Bristol) タイトル： Determinacy within Second Order Arithmetic
Abstract: It was proven by H. Friedman in 1971 that the determinacy of two person perfect information games played on integers at the 5th level of the arithmetic hierarchy (so Sigma^0_5) would require the use of set theoretical axioms such as the Power Set Axiom. (This was improved by Martin to the 4th level.)
Strategies for Sigma^0_k games for k =3D 1,2 were located in the Goedel L-hierachy by a folklore result (k=3D1) and Solovay (for k=3D2). We give a theorem on this kind for the last case left in the arithmetical hierarchy provable in analysis, thus for k=3D3.
More recently Montalban and Shore have calculated the exact strength of determinacy provable in Second Order Number theory. We give some conjectures and a report on recent work that seeks to lift Montalban-Shore to the corresponding theory that includes a single measurable cardinal.