Normann, Dag - The extensional realizability model of continuous functionals and three weakly non-constructive classical theorems

lmcs:1174 - Logical Methods in Computer Science, March 16, 2015, Volume 11, Issue 1
The extensional realizability model of continuous functionals and three weakly non-constructive classical theorems

Authors: Normann, Dag

We investigate wether three statements in analysis, that can be proved classically, are realizable in the realizability model of extensional continuous functionals induced by Kleene's second model $K_2$. We prove that a formulation of the Riemann Permutation Theorem as well as the statement that all partially Cauchy sequences are Cauchy cannot be realized in this model, while the statement that the product of two anti-Specker spaces is anti-Specker can be realized.


Source : oai:arXiv.org:1502.02388
DOI : 10.2168/LMCS-11(1:8)2015
Volume: Volume 11, Issue 1
Published on: March 16, 2015
Submitted on: March 29, 2013
Keywords: Computer Science - Logic in Computer Science,Mathematics - Logic


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