Coquand, Thierry and Mannaa, Bassel - The Independence of Markov's Principle in Type Theory

lmcs:3859 - Logical Methods in Computer Science, August 15, 2017, Volume 13, Issue 3
The Independence of Markov's Principle in Type Theory

Authors: Coquand, Thierry and Mannaa, Bassel

In this paper, we show that Markov's principle is not derivable in dependent type theory with natural numbers and one universe. One way to prove this would be to remark that Markov's principle does not hold in a sheaf model of type theory over Cantor space, since Markov's principle does not hold for the generic point of this model. Instead we design an extension of type theory, which intuitively extends type theory by the addition of a generic point of Cantor space. We then show the consistency of this extension by a normalization argument. Markov's principle does not hold in this extension, and it follows that it cannot be proved in type theory.


Source : oai:arXiv.org:1602.04530
DOI : 10.23638/LMCS-13(3:10)2017
Volume: Volume 13, Issue 3
Published on: August 15, 2017
Submitted on: August 15, 2017
Keywords: Computer Science - Logic in Computer Science,F.4.1


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