منابع مشابه
On relatively analytic and Borel subsets
Define z to be the smallest cardinality of a function f : X → Y withX, Y ⊆ 2 such that there is no Borel function g ⊇ f . In this paper we prove that it is relatively consistent with ZFC to have b < z where b is, as usual, smallest cardinality of an unbounded family in ω. This answers a question raised by Zapletal. We also show that it is relatively consistent with ZFC that there exists X ⊆ 2 s...
متن کاملDisjoint Borel functions
For each a ∈ ω, we define a Baire class one function fa : ω → ω which encodes a in a certain sense. We show that for each Borel g : ω → ω, fa ∩ g = ∅ implies a ∈ ∆1(c) where c is any code for g. We generalize this theorem for g in a larger pointclass Γ. Specifically, when Γ = ∆2, a ∈ L[c]. Also for all n ∈ ω, when Γ = ∆3+n, a ∈M1+n(c).
متن کاملTowers of Borel Functions
We give mathematical reformulations of the cardinals p and t in terms of families of Borel functions. As an application we show that t is invariant under the addition of a single Cohen real.
متن کاملWhen are Borel functions Baire functions ?
The following two theorems give the flavour of what will be proved. THEOREM. Let Y be a complete metric space. Then the families of first Baire class functions and of first Borel class functions from [0, 1] to Y coincide if and only if Y is connected and locally connected. THEOREM. Let Y be a separable metric space. Then the families of second Baire class functions and of second Borel class fun...
متن کاملEffective Borel measurability and reducibility of functions
The investigation of computational properties of discontinuous functions is an important concern in computable analysis. One method to deal with this subject is to consider effective variants of Borel measurable functions. We introduce such a notion of Borel computability for single-valued as well as for multi-valued functions by a direct effectivization of the classical definition. On Baire sp...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 2004
ISSN: 0026-2285
DOI: 10.1307/mmj/1091112076