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MARKOV’S PRINCIPLE AND SUBSYSTEMS OF INTUITIONISTIC ANALYSIS

  • JOAN RAND MOSCHOVAKIS (a1)

Abstract

Using a technique developed by Coquand and Hofmann [3] we verify that adding the analytical form MP1: $\forall \alpha (\neg \neg \exists {\rm{x}}\alpha ({\rm{x}}) = 0 \to \exists {\rm{x}}\alpha ({\rm{x}}) = 0)$ of Markov’s Principle does not increase the class of ${\rm{\Pi }}_2^0$ formulas provable in Kleene and Vesley’s formal system for intuitionistic analysis, or in subsystems obtained by omitting or restricting various axiom schemas in specified ways.

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[1]Avigad, J., Interpreting classical theories in constructive ones, this Journal, vol. 65 (2000), pp. 17851812.
[2]Bridges, D. and Richman, F., Varieties of Constructive Mathematics, London Mathematical Society Lecture Note Series, vol. 97, Cambridge University Press, Cambridge, 1987.
[3]Coquand, T. and Hofmann, M., A new method for establishing conservativity of classical systems over their intuitionistic version. Mathematical Structures in Computer Science, vol. 9 (1999), pp. 323333.
[4]Kleene, S. C., Introduction to Metamathematics, van Nostrand, Princeton, NJ, 1952.
[5]Kleene, S. C., Formalized Recursive Functionals and Formalized Realizability, Memoirs, vol. 89, American Mathematical Society, Providence, RI, 1969.
[6]Kleene, S. C. and Vesley, R. E., The Foundations of Intuitionistic Mathematics, Especially in Relation to Recursive Functions, North Holland, Amsterdam, 1965.
[7]Vafeiadou, G., Formalizing constructive analysis: A comparison of minimal systems and a study of uniqueness principles, Ph.D. thesis, National and Kapodistrian University of Athens, 2012.
[8]Vafeiadou, G., A comparison of minimal systems for constructive analysis, arXiv:1808.000383.

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MARKOV’S PRINCIPLE AND SUBSYSTEMS OF INTUITIONISTIC ANALYSIS

  • JOAN RAND MOSCHOVAKIS (a1)

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