Simple Saturated Sets for Disjunction and Second-Order Existential Quantification

  • Makoto Tatsuta
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4583)


This paper gives simple saturated sets for disjunction and second-order existential quantification by using the idea of segments in Prawitz’s strong validity. Saturated sets for disjunction are defined by Pi-0-1 comprehension and those for second-order existential quantification are defined by Sigma-1-1 comprehension. Saturated-set semantics and a simple strong normalization proof are given to the system with disjunction, second-order existential quantification, and their permutative conversions. This paper also introduces the contraction property to saturated sets, which gives us saturated sets closed under union. This enables us to have saturated-set semantics for the system with union types, second-order existential types, and their permutative conversions, and prove its strong normalization.


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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Makoto Tatsuta
    • 1
  1. 1.National Institute of Informatics, 2-1-2 Hitotsubashi, Tokyo 101-8430Japan

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