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More about relatively lawless sequences

  • Joan Rand Moschovakis (a1)

Abstract

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 lawlessness 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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[1]Kleene, S. C. [1952], Introduction to metamathematics, North-Holland, Amsterdam.
[2]Kleene, S. C. and Vesley, R. E. [1965], The foundations of intuitionistic mathematics, especially in relation to recursive functions, North-Holland, Amsterdam.
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[6]Moschovakis, J. R. [1987], Relative lawlessness in intuitionistic analysis, this Journal, vol. 52. pp. 68–88.
[7]Moschovakis, J. R. [1993], An intuitionistic theory of lawlike, choice and lawless sequences, Logic Colloquium ’90, Lecture Notes in Logic 2 (Oikkonen, J. and Väänänen, J., editors), Springer-Verlag, pp. 191–209.
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  • Joan Rand Moschovakis (a1)

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