A constructive version of the Lusin Separation Theorem
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Invited Talks and Tutorials A Constructive Version of the Lusin Separation Theorem
The Lusin Separation Theorem is one of the fundamental early results of classical descriptive set theory. It states that if A1, A2 are disjoint analytic subsets of Baire space then they are Borel separable. Yiannis Moschovakis gives two proofs in his book, “Descriptive Set Theory”. One proof is obviously highly non-constructive. The other would appear to be constructive and uses Bar Induction a...
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Bar Induction occupies a central place in Brouwerian mathematics. This note is concerned with the strength of Bar Induction on the basis of Constructive ZermeloFraenkel Set Theory, CZF. It is shown that CZF augmented by decidable Bar Induction proves the 1-consistency of CZF. This answers a question of P. Aczel who used Bar Induction to give a proof of the Lusin Separation Theorem in the constr...
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While there is a well-established notion of what a computable ordinal is, the question which functions on the countable ordinals ought to be computable has received less attention so far. We propose a notion of computability on the space of countable ordinals via a representation in the sense of computable analysis. The computability structure is characterized by the computability of four speci...
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It is often demonstrated that Brouwer’s fixed point theorem can not be constructively proved. Therefore, Kakutani’s fixed point theorem, the Fan-Glicksberg fixed point theorem and the existence of a pure strategy Nash equilibrium in a strategic game with continuous (infinite) strategies and quasi-concave payoff functions also can not be constructively proved. On the other hand, however, Sperner...
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تاریخ انتشار 2006