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2 results

  • MARKOV’S PRINCIPLE AND SUBSYSTEMS OF INTUITIONISTIC ANALYSIS

  • JOAN RAND MOSCHOVAKIS
  • Journal:
    The Journal of Symbolic Logic / Volume 84 / Issue 2 / June 2019
    Published online by Cambridge University Press:
    26 February 2019, pp. 870-876
    Print publication:
    June 2019

  • 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.

  • SEPARATING FRAGMENTS OF WLEM, LPO, AND MP

  • MATT HENDTLASS, ROBERT LUBARSKY
  • Journal:
    The Journal of Symbolic Logic / Volume 81 / Issue 4 / December 2016
    Published online by Cambridge University Press:
    01 December 2016, pp. 1315-1343
    Print publication:
    December 2016

  • We separate many of the basic fragments of classical logic which are used in reverse constructive mathematics. A group of related Kripke and topological models is used to show that various fragments of the Weak Law of the Excluded Middle, the Limited Principle of Omniscience, and Markov’s Principle, including Weak Markov’s Principle, do not imply each other.