Kobe Colloquium on Logic, Statistics and Informatics
以下の要領でコロキウムを開催します。
日時：2013年5月1日（水）15:00-16:30 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：Rod Downey (Victoria University of Wellington, New Zealand)
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題目：Effectively in Abelian Group Theory
アブストラクト：The effectiveness of the theory of abelian groups has been long studied beginning with the work of Mal'cev in the 60's. Nevertheless many problems remain. In this lecture I will discuss ongoing work on questions of effectiveness of categoricity and presentability for computable torsion-free abelian groups and for p-groups. For example, for categoricity, general problem is impossible; for example Downey and Montalban showed that the isomorphism problem for torsion-free abelian groups is Sigma_1^1-complete. The principle difficulty lies in the lack of invariants. However, where there are some invariants there we can salvage some effectiveness. The groups we look at are the completely decomposable ones, which have decompositions of the form oplus_{i in omega} G_i with G_i a subgroup of the additive group of the rationals. Such groups are called homogeneous if G_i=H for all i. Alexander Melnikov and the author have shown that homogeneous computable completely decomposable groups are always Delta_3^0 categorical, this bound is sharp, and have classified when the groups are Delta_2^0 categorical in terms of what are called semilow sets. In more recent work, we have shown that every computable completely decomposable group is Delta_5^0 categorical and that this bound is sharp. Additionally we can show that the index set of such groups is Sigma_7^0. I will also describe ongoing work on Ulm's Theorem.
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交通：阪急六甲駅またはJR六甲道駅から神戸市バス36系統「鶴甲団地」 行きに乗車，「神大本部工学部前」停留所下車，徒歩すぐ． http://www.kobe-u.ac.jp/info/access/rokko/rokkodai-dai2.htm
連絡先：ブレンドレ ヨーグ [email protected]