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Set theory, higher order logic or both?

  • Mike Gordon
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1125)

Abstract

The majority of general purpose mechanised proof assistants support versions of typed higher order logic, even though set theory is the standard foundation for mathematics. For many applications higher order logic works well and provides, for specification, the benefits of type-checking that are well-known in programming. However, there are areas where types get in the way or seem unmotivated. Furthermore, most people with a scientific or engineering background already know set theory, but not higher order logic. This paper discusses some approaches to getting the best of both worlds: the expressiveness and standardness of set theory with the efficient treatment of functions provided by typed higher order logic.

Keywords

Type Versus Type Theory Inaccessible Cardinal Simple Type Theory Standard Foundation 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Mike Gordon
    • 1
  1. 1.University of Cambridge Computer LaboratoryCambridgeU.K.

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