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Decomposing Borel functions and structure at finite levels of the Baire hierarchy

Janusz Pawlikowski & Marcin Sabok

Annals of Pure and Applied Logic 163 (12):1748-1764 (2012)

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(1 other version)A very discontinuous borel function.Juris Steprāns - 1993 - Journal of Symbolic Logic 58 (4):1268 - 1283.details It is shown to be consistent that the reals are covered by ℵ1 meagre sets yet there is a Baire class 1 function which cannot be covered by fewer than ℵ2 continuous functions. A new cardinal invariant is introduced which corresponds to the least number of continuous functions required to cover a given function. This is characterized combinatorially. A forcing notion similar to, but not equivalent to, superperfect forcing is introduced. Download Export citation Bookmark 4 citations
Decomposing baire functions.J. Cichoń, M. Morayne, J. Pawlikowski & S. Solecki - 1991 - Journal of Symbolic Logic 56 (4):1273 - 1283.details We discuss in the paper the following problem: Given a function in a given Baire class, into "how many" (in terms of cardinal numbers) functions of lower classes can it be decomposed? The decomposition is understood here in the sense of the set-theoretical union. Download Export citation Bookmark 4 citations
Baire reductions and good Borel reducibilities.Luca Motto Ros - 2010 - Journal of Symbolic Logic 75 (1):323-345.details In [9] we have considered a wide class of "well-behaved" reducibilities for sets of reals. In this paper we continue with the study of Borel reducibilities by proving a dichotomy theorem for the degree-structures induced by good Borel reducibilities. This extends and improves the results of [9] allowing to deal with a larger class of notions of reduction (including, among others, the Baire class ξ functions). Download Export citation Bookmark 6 citations

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