共查询到20条相似文献，搜索用时 15 毫秒
1.
V. L. Selivanov 《Algebra and Logic》2005,44(2):95-108
We deal with the Borel and difference hierarchies in the space P of all subsets of endowed with the Scott topology. (The spaces P and 2
coincide set-theoretically but differ topologically.) We look at the Wadge reducibility in P. The results obtained are applied to the problem of characterizing 1-terms t which satisfy C = t(
1
0
) for a given Borel-Wadge class C. We give its solution for some levels of the Wadge hierarchy, in particular, all levels of the Hausdorff difference hierarchy. Finally, we come up with a discussion of some relevant facts and open questions.__________Translated from Algebra i Logika, Vol. 44, No. 2, pp. 173–197, March–April, 2005. 相似文献
2.
Luca Motto Ros 《Mathematical Logic Quarterly》2011,57(1):95-112
We present a general way of defining various reduction games on ω which “represent” corresponding topologically defined classes of functions. In particular, we will show how to construct games for piecewise defined functions, for functions which are pointwise limit of certain sequences of functions and for Γ ‐measurable functions. These games turn out to be useful as a combinatorial tool for the study of general reducibilities for subsets of the Baire space [10] (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
3.
Michael Hrusá k Beatriz Zamora Avilé s 《Proceedings of the American Mathematical Society》2005,133(11):3429-3435
We investigate which definable separable metric spaces are countable dense homogeneous (CDH). We prove that a Borel CDH space is completely metrizable and give a complete list of zero-dimensional Borel CDH spaces. We also show that for a Borel the following are equivalent: (1) is in , (2) is CDH and (3) is homeomorphic to or to . Assuming the Axiom of Projective Determinacy the results extend to all projective sets and under the Axiom of Determinacy to all separable metric spaces. In particular, modulo a large cardinal assumption it is relatively consistent with ZF that all CDH separable metric spaces are completely metrizable. We also answer a question of Stepr ns and Zhou, by showing that is not CDH.
4.
5.
Victor L. Selivanov 《Mathematical Logic Quarterly》2005,51(1):45-61
We establish some results on the Borel and difference hierarchies in φ‐spaces. Such spaces are the topological counterpart of the algebraic directed‐complete partial orderings. E.g., we prove analogs of the Hausdorff Theorem relating the difference and Borel hierarchies and of the Lavrentyev Theorem on the non‐collapse of the difference hierarchy. Some of our results generalize results of A. Tang for the space Pω. We also sketch some older applications of these hierarchies and present a new application to the question of characterizing the ω‐ary Boolean operations generating a given level of the Wadge hierarchy from the open sets. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
6.
7.
Takako Nemoto 《Mathematical Logic Quarterly》2009,55(2):154-176
In this paper we study the logical strength of the determinacy of infinite binary games in terms of second order arithmetic. We define new determinacy schemata inspired by the Wadge classes of Polish spaces and show the following equivalences over the system RCA0*, which consists of the axioms of discrete ordered semi‐rings with exponentiation, Δ10 comprehension and Π00 induction, and which is known as a weaker system than the popularbase theory RCA0: 1. Bisep(Δ10, Σ10)‐Det* ? WKL0, (1) 2. Bisep(Δ10, Σ20)‐Det* ? ATR0 + Σ11 induction, (2) 3. Bisep(Σ10, Σ20)‐Det* ? Sep(Σ10, Σ20)‐Det* ? Π11‐CA0, (3) 4. Bisep(Δ20, Σ20)‐Det* ? Π11‐TR0, (4) where Det* stands for the determinacy of infinite games in the Cantor space (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
8.
Assuming , the hierarchy of norms is a wellordered structure of equivalence classes of ordinal-valued maps. We define operations on the hierarchy of norms, in particular an operation that dominates multiplication as an operation on the ranks of norms, and use these operations to establish a considerably improved lower bound for the length of the hierarchy of norms. 相似文献
9.
In this paper, we show that, for each p 〉 1, there are continuum many Borel equivalence relations between Rω/l1 and Rω/p ordered by ≤B which are pairwise Borel incomparable. 相似文献
10.
A function from the plane to the plane is axial if it does not change one coordinate. We show that every Borel permutation of the plane is a superposition of 11 Borel axial permutations. 相似文献
11.
Randall Dougherty Greg Hjorth 《Transactions of the American Mathematical Society》1999,351(5):1835-1844
We show that, for , the relation of -equivalence between infinite sequences of real numbers is Borel reducible to the relation of -equivalence (i.e., the Borel cardinality of the quotient is no larger than that of ), but not vice versa. The Borel reduction is constructed using variants of the triadic Koch snowflake curve; the nonreducibility in the other direction is proved by taking a putative Borel reduction, refining it to a reduction map that is not only continuous but `modular,' and using this nicer map to derive a contradiction.
12.
Su Gao 《Proceedings of the American Mathematical Society》2002,130(3):863-874
We analyze the technique used by Adams and Kechris (2000) to obtain their results about Borel reducibility of countable Borel equivalence relations. Using this technique, we show that every equivalence relation is Borel reducible to the Borel bi-reducibility of countable Borel equivalence relations. We also apply the technique to two other classes of essentially uncountable Borel equivalence relations and derive analogous results for the classification problem of Borel automorphisms.
13.
In this article we prove that an algebraic Lie algebra over an algebraically closed field of characteristic 0 is complete if its Borel subalgebras are complete. Thus the study on complete Lie algebras may somewhat be reduced to that on solvable complete ones. 相似文献
14.
15.
If is an equivalence relation on a standard Borel space , then we say that is Borel reducible to if there is a Borel function such that . An equivalence relation on a standard Borel space is Borel if its graph is a Borel subset of . It is countable if each of its equivalence classes is countable. We investigate the complexity of Borel reducibility of countable Borel equivalence relations on standard Borel spaces. We show that it is at least as complex as the relation of inclusion on the collection of Borel subsets of the real line. We also show that Borel reducibility is -complete. The proofs make use of the ergodic theory of linear algebraic groups, and more particularly the superrigidity theory of R. Zimmer.
16.
Michael Ray Oliver 《Proceedings of the American Mathematical Society》2006,134(8):2419-2425
The Borel cardinality of the quotient of the power set of the natural numbers by the ideal of asymptotically zero-density sets is shown to be the same as that of the equivalence relation induced by the classical Banach space . We also show that a large collection of ideals introduced by Louveau and Velickovic, with pairwise incomparable Borel cardinality, are all Borel reducible to . This refutes a conjecture of Hjorth and has facilitated further work by Farah.
17.
18.
M. G. Nadkarni 《Proceedings Mathematical Sciences》1990,100(3):203-220
A necessary and sufficient condition is given for a Borel automorphism on a standard Borel space to admit an invariant probability
measure. 相似文献
19.
Computable Homogeneous Boolean Algebras and a Metatheorem 总被引：1，自引：0，他引：1
P. E. Alaev 《Algebra and Logic》2004,43(2):73-87
We consider computable homogeneous Boolean algebras. Previously, countable homogeneous Boolean algebras have been described up to isomorphism and a simple criterion has been found for the existence of a strongly constructive (decidable) isomorphic copy for such. We propose a natural criterion for the existence of a constructive (computable) isomorphic copy. For this, a new hierarchy of
-computable functions and sets is introduced, which is more delicate than Feiner's. Also, a metatheorem is proved connecting computable Boolean algebras and their hyperarithmetical quotient algebras. 相似文献
20.
John Isbell 《Proceedings of the American Mathematical Society》1998,126(8):2477-2479
All Borel classes of sublocales of the real line after the first ambiguous class (in particular, the limit ambiguous classes) have proper (=irreducible) representatives.