Relative lawlessness in intuitionistic analysis

Relative lawlessness in intuitionistic analysis

This paper introduces, as an alternative to the (absolutely) lawless sequences of Kreisel and Troelstra, a notion of choice sequence lawless with respect to a given class D of lawlike sequences. For countable D, the class of D-lawless sequences is comeager in the sense of Baire. If a particular well...

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Veröffentlicht in:The Journal of symbolic logic 1987-03, Vol.52 (1), p.68-88
1. Verfasser: Moschovakis, Joan Rand
Format: Artikel
Sprache:eng
Schlagworte:
Axioms
Choice sequences
Induction assumption
Integers
Intuitionistic type theory
Mathematical logic
Mathematical sequences
Natural numbers
Numerals
Reasoning
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description This paper introduces, as an alternative to the (absolutely) lawless sequences of Kreisel and Troelstra, a notion of choice sequence lawless with respect to a given class D of lawlike sequences. For countable D, the class of D-lawless sequences is comeager in the sense of Baire. If a particular well-ordered class F of sequences, generated by iterating definability over the continuum, is countable then the F-lawless, sequences satisfy the axiom of open data and the continuity principle for functions from lawless to lawlike sequences, but fail to satisfy Troelstra's extension principle. Classical reasoning is used.
doi_str_mv 10.2307/2273863
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1943-5886
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subjects Axioms
Choice sequences
Induction assumption
Integers
Intuitionistic type theory
Mathematical logic
Mathematical sequences
Natural numbers
Numerals
Reasoning
title Relative lawlessness in intuitionistic analysis
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