みなさま

新井@千葉大学です。 千葉 logic seminar の第5回のお知らせです。

どなたでも参加できますので どうぞ気軽にいらっしゃって下さい。

問合せ先 新井敏康（千葉大学） [email protected]

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日時：3月13日(金)13:30-15:00 場所：千葉大学理学部2号館105号室 アクセスは http://www.chiba-u.ac.jp/campus_map/nishichiba/index.html の地図の黄色い理学部の中で数字2が付いている建物の1階です。

Speaker: Stan Wainer (Leeds UK)

Title: A miniaturized predicativity

Abstract: This talk attempts to characterize those recursive functions which are "predictably terminating" according to a finitistic point of view. The basis of the work is Leivant's (1995) theory of ramified induction over N, which has elementary recursive strength. It has been redeveloped and extended in various ways by many people. Eg. Spoors & W. (2012) built a hierarchy of ramified "input-output" theories whose strengths correspond to the levels of the Grzegorczyk hierarchy. Here, a further extension of this hierarchy is developed, with one additional input level on top (level omega). The underlying logic is an autonomously generated infinitary calculus with arbitrary finitely-many stratification levels of numerical inputs and a ramified Repetition Rule. The autonomous control on allowable ordinals is based on a weak (finitistic) notion of "pointwise transfinite induction". It turns out that the ordinal of this theory is then Gamma-0; the provably computable functions are those which are resource-bounded by the slow growing hierarchy; and these are the functions elementary recursive in the Ackermann function.

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