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INTUITIONISTIC ANALYSIS AT THE END OF TIME

Published online by Cambridge University Press:  04 December 2017

JOAN RAND MOSCHOVAKIS
JOAN RAND MOSCHOVAKIS*
Affiliation:
DEPARTMENT OF MATHEMATICS OCCIDENTAL COLLEGE LOS ANGELES, CA90041, USAE-mail: joan.rand@gmail.comURL: http://www.math.ucla.edu/∼joan/
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Abstract

Kripke recently suggested viewing the intuitionistic continuum as an expansion in time of a definite classical continuum. We prove the classical consistency of a three-sorted intuitionistic formal system IC, simultaneously extending Kleene’s intuitionistic analysis I and a negative copy C° of the classically correct part of I, with an “end of time” axiom ET asserting that no choice sequence can be guaranteed not to be pointwise equal to a definite (classical or lawlike) sequence. “Not every sequence is pointwise equal to a definite sequence” is independent of IC. The proofs are by Crealizability interpretations based on classical ω-models ${\cal M}$ = $\left( {\omega ,{\cal C}} \right)$ of C°.

Keywords

03F2503F5003F55intuitionistic analysiscountable choicenegative interpretationreadabilityomega-modelclassical analysisconsistency proof
Type
Articles
Information
Bulletin of Symbolic Logic , Volume 23 , Issue 3 , September 2017 , pp. 279 - 295
Copyright
Copyright © The Association for Symbolic Logic 2017 

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References

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