author={Matthew Hendtlass and Robert S. Lubarsky},
  journal={The Journal of Symbolic Logic},
  pages={1315 - 1343}
Abstract 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. 

Lifschitz Realizability as a Topological Construction Michael Rathjen and

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Equivalents of disjunctive Markov's principle

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Point-Free Spectra of Linear Spreads

  • D. Wessel
  • Mathematics
    Mathesis Universalis, Computability and Proof
  • 2019
Scott’s multiple-conclusion entailment relations, originally conceived as a means to clarify several aspects of many-valued logic, and later put to great use in a revised Hilbert programme for

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In [34] Georg Kreisel reflected at length on Church’s Thesis CT, the principle proposed in 1936 by Alonzo Church ([9]) as a definition: “We now define the notion . . . of an effectively calculable

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A number of nonconstructive mathematical theorems are classified by means of a hierarchy of logical principles which are not included in intuitionistic logic by giving insights in both the scope of limit computable mathematics and its subsystems, and the nature of the theoreMS of classical mathematics considered.

On Weak Markov's Principle

We show that the so-called weak Markov's principle (WMP) which states that every pseudo-positive real number is positive is underivable in ω ≔ E-HAω + AC. Since ω allows one to formalize (atl eastl

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It is proved that parallelized LLPO is equivalent to Weak Kőnig's Lemma and hence to the Hahn–Banach Theorem in this new and very strong sense and any single-valued weakly computable operation is already computable in the ordinary sense.

Constructive Zermelo-Fraenkel set theory and the limited principle of omniscience

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Realizing Brouwer's Sequences

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