منابع مشابه
Towers 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 کاملTowers of Measurable Functions
We formulate variants of the cardinals f, p and t in terms of families of measurable functions, in order to examine the effect upon these cardinals of adding one random real.
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 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: Proceedings of the American Mathematical Society
سال: 1999
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-99-05013-3