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A Typed λ-calculus and Girard’s Model of Ptykes

  • Peter Päppinghaus

Abstract

In a fundamental paper inaugurating Π1/2-logic Girard (1981) introduced the notion of a dilator as a functor from the category of ordinals into itself preserving direct limits and pull-backs. In Chapter 12 of a forthcoming book (Girard (198.)) he generalizes this notion to all finite types. For every finite type σ a category PTσ is defined whose objects form a (proper) class Ptσ and are called ptykes of type σ. In annex 12.A of his book Girard proves the ptykes of finite types to be a model of a variant T’ of Gödel’s T. Using this new model he proposes an intrinsic “ordinal assignment” to terms of T’. To (closed) terms of type o → o, in particular, their value at ω is assigned. We are interested in determining these values.

Keywords

Finite Type Direct Limit Proof Theory Characteristic Term Principal Constituent 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Barendregt, H. P., 1981, “The Lambda Calculus,” North-HoHand, Amsterdam.Google Scholar
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Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • Peter Päppinghaus
    • 1
  1. 1.Institut für MathematikUniversität HannoverHannoverGermany

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