Homogeneous Borel Sets of Ambiguous Class Two
نویسنده
چکیده
We describe and characterize all homogeneous subsets of the Cantor set which are both an F„s and a GSo; it turns out that there are wx such spaces.
منابع مشابه
On Winning Conditions of High Borel Complexity in Pushdown Games
In a recent paper [19, 20] Serre has presented some decidable winning conditions ΩA1B...BAnBAn+1 of arbitrarily high finite Borel complexity for games on finite graphs or on pushdown graphs. We answer in this paper several questions which were raised by Serre in [19, 20]. We study classes Cn(A), defined in [20], and show that these classes are included in the class of non-ambiguous context free...
متن کاملBorel homomorphisms of smooth σ-ideals
Given a countable Borel equivalence relation E on a Polish space, let IE denote the σ-ideal generated by the Borel partial transversals of E. We show that there is a Borel homomorphism from IE to IF if and only if there is a smooth-to-one Borel homomorphism from a finite index Borel subequivalence relation of E to F . As a corollary, we see that IE is homogeneous in the sense of Zapletal (2007,...
متن کاملClassifying Countable Boolean Terms
Let {Σα}α<ω1 , where ω1 is the first non-countable ordinal, denote the Borel hierarchy of subsets of the Cantor space 2. As usual, Πα denotes the dual class for Σα while ∆ 0 α = Σ 0 α ∩Πα — the corresponding ambiguous class. Let B = ∪α<ω1Σα denote the class of all Borel sets. The levels of Borel hierarchy, as well as many other classes of interest for descriptive set theory, may be defined by m...
متن کاملPotential Wadge classes
Let Γ be a Borel class, or a Wadge class of Borel sets, and 2≤d≤ω a cardinal. We study the Borel subsets of R that can be made Γ by refining the Polish topology on the real line. These sets are called potentially Γ. We give a test to recognize potentially Γ sets. 2010 Mathematics Subject Classification. Primary: 03E15, Secondary: 54H05, 28A05, 26A21
متن کاملOn the Extension of Borel Measures
The class of Borel sets in a locally compact space is the cr-ring generated by the compact sets [3, p. 219], while the class of weakly Borel sets is the (r-algebra generated by the closed sets [2]. The object of this note is to show that any measure defined on the class of Borel sets may be extended to the class of weakly Borel sets in a simple and canonical way (Theorem 1). There is a useful a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010