Intuitionistic L

  • Robert S. Lubarsky
Part of the Progress in Computer Science and Applied Logic book series (PCS, volume 12)


The goal of this paper is to develop the basics of IL, that is, L under intuitionistic reasoning. The highlights are that (under IZF) IL is a model of V = L and also of IZF. While these are not exciting results classically, they and their associated lemmas are examples of the phenomenon that classical trivialities can become sticky intuitionistically, when they are not downright false.


Kripke Model Main Lemma Intuitionistic Reasoning Decode Function Easy Corollary 
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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  1. [FS]
    Friedman, H. and A. Scedrov [1985], The lack of definable witnesses and provably recursive functions in intuitionistic set theories, Advances in Math, 57, 1–13.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [Gl]
    Grayson, R. [1982], Constructive well-orderings, Zeitschrift f. Math. Logik u. Grundlagen d. Math. 28, 495–504.MathSciNetzbMATHCrossRefGoogle Scholar
  3. [G2]
    Grayson, R. [1979], Hey ting-valued models for intuitionistic set theory, Applications of Sheaves ( Fourman, Mulvey and Scott, eds.), Springer Lecture Notes in Mathematics 753, 402–414.Google Scholar
  4. [Li]
    Lipton, J., Readability, set theory, and term extraction, in The Curry-Howard Isomorphism. To appear.Google Scholar
  5. [Lu]
    Lubarsky, R., IKP and friends. To appear.Google Scholar
  6. [M]
    McCarty, C. [D]. [1986], Realizability and recursive set theory, Annals of Pure and Applied Logic, 32, 153–183.MathSciNetzbMATHCrossRefGoogle Scholar
  7. [P]
    Powell, W. [1975], Extending Gödel’s negative interpretation of ZF, J. of Symbolic Logic 40, 221–229.zbMATHCrossRefGoogle Scholar
  8. [S]
    Scedrov, A. [1985], Intuitionistic set theory, Harvey Friedman’s Research on the Foundations of Mathematics, North-Holland, 257–284.Google Scholar

Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Robert S. Lubarsky
    • 1
  1. 1.Dept. of MathematicsFranklin and Marshall CollegeLancasterUSA

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