منابع مشابه
Disjoint 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).
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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.
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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...
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We introduce a new information-theoretic primitive called programmable hash functions (PHFs). PHFs can be used to program the output of a hash function such that it contains solved or unsolved discrete logarithm instances with a certain probability. This is a technique originally used for security proofs in the random oracle model. We give a variety of standard model realizations of PHFs (with ...
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: The Annals of Probability
سال: 1978
ISSN: 0091-1798
DOI: 10.1214/aop/1176995576