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INTUITIONISTIC ANALYSIS AT THE END OF TIME
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- Journal:
- Bulletin of Symbolic Logic / Volume 23 / Issue 3 / September 2017
- Published online by Cambridge University Press:
- 04 December 2017, pp. 279-295
- Print publication:
- September 2017
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- Article
- Export citation
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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°.
