[logic-ml] Kobe Colloquium (Feb. 18, 2013)

[Sakae Fuchino]

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.

-- 
best regards                                    Saka\'e Fuchino (渕野 昌)
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Kobe University 
Graduate School of System Informatics 
Rokko-dai 1-1, Nada, Kobe 
657-8501 Japan

                   e-mail: fuchino at diamond.kobe-u.ac.jp 
                   web page: http://kurt.scitec.kobe-u.ac.jp/~fuchino/
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