Borel completeness of some א0-stable theories
نویسندگان
چکیده
We study א0-stable theories, and prove that if T either has eniDOP or is eni-deep, then its class of countable models is Borel complete. We introduce the notion of λ-Borel completeness and prove that such theories are λ-Borel complete. Using this, we conclude that an א0-stable theory satisfies I∞,א0(T, λ) = 2 λ for all cardinals λ if and only if T either has eni-DOP or is eni-deep.
منابع مشابه
The Borel Complexity of Isomorphism for Some First-order Theories
Title of dissertation: THE BOREL COMPLEXITY OF ISOMORPHISM FOR SOME FIRST-ORDER THEORIES Richard Rast, Doctor of Philosophy, 2016 Dissertation directed by: Professor Michael C. Laskowski Department of Mathematics In this work we consider several instances of the following problem: “how complicated can the isomorphism relation for countable models be?” Using the Borel reducibility framework from...
متن کاملCompleteness in Probabilistic Metric Spaces
The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining p...
متن کاملSpecial groups whose isometry relation is a finite union of cosets
א0-stable א0-categorical linked quaternionic mappings are studied and are shown to correspond (in some sense) to special groups which are א0stable, א0-categorical, satisfy AP (3) and have finite 2-symbol length. They are also related to special groups whose isometry relation is a finite union of cosets, which are then considered on their own, as well as their links with pseudofinite, profinite ...
متن کاملBorel chromatic number of closed graphs
We construct, for each countable ordinal ξ, a closed graph with Borel chromatic number two and Baire class ξ chromatic number א0. 2010 Mathematics Subject Classification. Primary: 03E15, Secondary: 54H05
متن کاملMeasurable chromatic numbers
We show that if add(null) = c, then the globally Baire and universally measurable chromatic numbers of the graph of any Borel function on a Polish space are equal and at most three. In particular, this holds for the graph of the unilateral shift on [N]N, although its Borel chromatic number is א0. We also show that if add(null) = c, then the universally measurable chromatic number of every treei...
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 2013