Polish group actions, nice topologies, and admissible sets
نویسنده
چکیده
Let G be a closed subgroup of S∞ and X be a Polish G-space. To each x ∈ X we associate an admissible set Ax and show how questions about X which involve Baire category, can be formalized in Ax.
منابع مشابه
Polish group actions and admissible sets
We generalize some model theory involving Hyp(M) and HF(M) to the case of actions of Polish groups on Polish spaces. In particular we obtain two variants of the Nadel’s theorem about relationships between Scott sentences and admissible sets.
متن کاملA Wadge hierarchy for second countable spaces
Wadge reducibility provides a rich and nice analysis of Borel sets in Polish zero dimensional spaces. However, outside this framework, reducibility by continuous functions was shown to be ill behaved in many important cases. We define a notion of reducibility for subsets of a second countable T0 topological space based on the notions of admissible representations and relatively continuous relat...
متن کاملSharper changes in topologies
LetG be a Polish group, τ a Polish topology on a spaceX, G acting continuously on (X, τ), with B ⊂ X G-invariant and in the Borel algebra generated by τ . Then there is a larger Polish topology τ ⊃ τ on X so that B is open with respect to τ, G still acts continuously on (X, τ), and τ has a basis consisting of sets that are of the same Borel rank as B relative to τ . 1
متن کاملSome new results on Borel irreducibility of equivalence relations ∗
We prove that orbit equivalence relations (ERs, for brevity) of generically turbulent Polish actions are not Borel reducible to ERs of a family which includes Polish actions of S∞, the group of all permutations of N, and is closed under the Fubini product modulo the ideal Fin of all finite sets, and some other operations. Our second main result shows that T2, an equivalence relation called “the...
متن کاملOn the non-existence of certain group topologies
Minimal Hausdorff (Baire) group topologies of certain groups of transformations naturally occurring in analysis are studied. The results obtained are subsequently applied to show that, e.g., the homeomorphism groups of the rational and of the irrational numbers carry no Polish group topology. In answer to a question of A.S. Kechris it is shown that that the group of Borel automorphisms of R can...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Math. Log. Q.
دوره 54 شماره
صفحات -
تاریخ انتشار 2008