More about relatively lawless sequences

Journal of Symbolic Logic 59 (3):813-829 (1994)
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In the author's Relative lawlessness in intuitionistic analysis [this JOURNAL. vol. 52 (1987). pp. 68-88] and An intuitionistic theory of lawlike, choice and lawless sequences [Logic Colloquium '90. Springer-Verlag. Berlin. 1993. pp. 191-209] a notion of lawless ness relative to a countable information base was developed for classical and intuitionistic analysis. Here we simplify the predictability property characterizing relatively lawless sequences and derive it from the new axiom of closed data (classically equivalent to open data) together with a natural principle of invariance under finite translation. We characterize relative lawlessness in terms of a notion of forcing. Finally, we study relative lawlessness on an arbitrary fan and show that the collection of lawless binary sequences (which is comeager in the sense of Baire) has probability measure zero. The reasoning is predominantly constructive



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Joan Rand Moschovakis
Occidental College

Citations of this work

A classical view of the intuitionistic continuum.Joan Rand Moschovakis - 1996 - Annals of Pure and Applied Logic 81 (1-3):9-24.
Analyzing realizability by Troelstra's methods.Joan Rand Moschovakis - 2002 - Annals of Pure and Applied Logic 114 (1-3):203-225.

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References found in this work

Constructivism in Mathematics, An Introduction.A. Troelstra & D. Van Dalen - 1991 - Tijdschrift Voor Filosofie 53 (3):569-570.
Formal systems for some branches of intuitionistic analysis.G. Kreisel - 1970 - Annals of Mathematical Logic 1 (3):229.
An interpretation of intuitionistic analysis.D. van Dalen - 1978 - Annals of Mathematical Logic 13 (1):1.
Introduction to Metamathematics.H. Rasiowa - 1954 - Journal of Symbolic Logic 19 (3):215-216.
Choice Sequences. A Chapter of Intuitionistic Mathematics.Richard Vesley - 1979 - Journal of Symbolic Logic 44 (2):275-276.

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