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400
On relatively analytic and Borel subsets
"... Define z to be the smallest cardinality of a function f: X → Y withX,Y ⊆ 2ω 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 ωω. This answers a question r ..."
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raised by Zapletal. We also show that it is relatively consistent with ZFC that there existsX ⊆ 2ω such that the Borel order ofX is bounded but there exists a relatively analytic subset of X which is not relatively coanalytic. This answers a question of Mauldin. The following is an equivalent definition
A SPACE WITH ONLY BOREL SUBSETS
"... Miklós Laczkovich (Budapest) asked if there exists a Haussdorff (or even normal) space in which every subset is Borel yet it is not meager. The motivation of the last condition is that under MAκ every subspace of the reals of cardinality κ has the property that all subsets are Fσ however Martin’s ax ..."
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Miklós Laczkovich (Budapest) asked if there exists a Haussdorff (or even normal) space in which every subset is Borel yet it is not meager. The motivation of the last condition is that under MAκ every subspace of the reals of cardinality κ has the property that all subsets are Fσ however Martin’s
NON-PERMUTATION INVARIANT BOREL QUANTIFIERS
"... Abstract. Every permutation invariant Borel subset of the space of countable structures is definable in Lω 1 ω by a theorem of Lopez-Escobar. We prove variants of this theorem relative to fixed relations and fixed non-permutation invariant quantifiers. Moreover we show that for every closed subgroup ..."
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Abstract. Every permutation invariant Borel subset of the space of countable structures is definable in Lω 1 ω by a theorem of Lopez-Escobar. We prove variants of this theorem relative to fixed relations and fixed non-permutation invariant quantifiers. Moreover we show that for every closed
NON-ISOMORPHISM INVARIANT BOREL QUANTIFIERS
"... Abstract. Every isomorphism invariant Borel subset of the space of structures on the natural numbers in a countable relational language is definable in Lω1ω by a theorem of Lopez-Escobar. We derive variants of this result for stabilizer subgroups of the symmetric group Sym(N) for families of relatio ..."
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Abstract. Every isomorphism invariant Borel subset of the space of structures on the natural numbers in a countable relational language is definable in Lω1ω by a theorem of Lopez-Escobar. We derive variants of this result for stabilizer subgroups of the symmetric group Sym(N) for families
Rigidity Theorems for Actions of Product Groups and Countable Borel Equivalence Relations
"... This paper is a contribution to the theory of countable Borel equivalence relations on standard Borel spaces. As usual, by a standard Borel space we mean a Polish (complete separable metric) space equipped with its #-algebra of Borel sets. An equivalence relation E on a standard Borel space X is Bor ..."
Arsenin -- Kunugui Theorem And Weak Forms Of Borel Bimeasurability
, 1999
"... . Let f be a Borel measurable mapping of a Luzin (i.e. absolute Borel) space L onto a metric space M such that f(F ) is a Borel subset of M if F is closed in L. We show that then M is also Luzin, that f \Gamma1 (y) is a K oe set for all, except for countably many, y 2 M , and that the Borel class ..."
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. Let f be a Borel measurable mapping of a Luzin (i.e. absolute Borel) space L onto a metric space M such that f(F ) is a Borel subset of M if F is closed in L. We show that then M is also Luzin, that f \Gamma1 (y) is a K oe set for all, except for countably many, y 2 M , and that the Borel
On the Borel Families of Subsets of Topological Spaces 1
"... Summary. This is the next Mizar article in a series aiming at complete ..."
Borel stay-in-a-set games 1
"... Abstract. Consider an n-person stochastic game with Borel state space S, compact metric action sets A1, A2,..., An, and law of motion q such that the integral under q of every bounded Borel measurable function depends measurably on the initial state x and continuously on the actions (a1, a2,..., an) ..."
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subset of a Polish space. Every player i has an action set Ai which is a compact metric space. The set P(Ai) of probability measures defined on the Borel subsets of Ai is given the usual weak topology and, hence, P(Ai) is also compact metrizable. Let
Results 1 - 10
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400
