Vassilis Gregoriades: A recursive theoretic view to the decomposability conjecture

Friday, May 30, 2014, 16.30
Seminar room 1.007, Mathematical Institute, University of Bonn

Speaker: Vassilis Gregoriades (Darmstadt)

Title: A recursive theoretic view to the decomposability conjecture

Abstract:

The decomposability conjecture states that every function from an analytic space to a separable metric space, for which the preimage of a Σ^0_{m+1} set is a Σ^0_{n+1} set, where m=1,2,…n, is decomposable into countably many Σ^0_{n-m+1}-measurable functions on Π^0_n domains. The aim of this talk is to present some recent results about this problem in zero-dimensional spaces. This is a joint work of Kihara and the speaker. The proofs make use of results from recursion theory and effective descriptive set theory, including a lemma by Kihara on canceling out Turing jumps and Louveau separation. We will first review the necessary material and then we will proceed to the proof of the new results. Moreover we will explain how these results can be extended from the context of zero-dimensional spaces to spaces of small inductive dimension.

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