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SEPARATING FRAGMENTS OF WLEM, LPO, AND MP

Published online by Cambridge University Press:  01 December 2016

MATT HENDTLASS  and
ROBERT LUBARSKY
MATT HENDTLASS
Affiliation:
DEPARTMENT OF MATHEMATICS AND STATISTICS UNIVERSITY OF CANTERBURY PRIVATE BAG 4800, CHRISTCHURCH, NEW ZEALAND E-mail: m.hendtlass@gmail.com
ROBERT LUBARSKY
Affiliation:
DEPARTMENT OF MATHEMATICAL SCIENCES FLORIDA ATLANTIC UNIVERSITY BOCA RATON, FL 33431, USA E-mail: rlubarsk@fau.edu
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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.

Keywords

03F5003C9003E7003H99omniscience principlesMarkov’s PrincipleWeak Markov’s Principleweak LEMtopological modelsKripke modelsnonstandard models

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Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 4 , December 2016 , pp. 1315 - 1343
Copyright
Copyright © The Association for Symbolic Logic 2016 

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