Borel structures and Borel theories
نویسندگان
چکیده
We show that there is a complete, consistent Borel theory which has no “Borel model” in the following strong sense: There is no structure satisfying the theory for which the elements of the structure are equivalence classes under some Borel equivalence relation and the interpretations of the relations and function symbols are Borel in the natural sense. We also investigate Borel isomorphisms between Borel structures.
منابع مشابه
Five-value rich lines, Borel directions and uniqueness of meromorphic functions
For a meromorphic function $f$ in the complex plane, we shall introduce the definition of five-value rich line of $f$, and study the uniqueness of meromorphic functions of finite order in an angular domain by involving the five-value rich line and Borel directions. Finally, the relationship between a five-value rich line and a Borel direction is discussed, that is, every Borel direction of $f$ ...
متن کاملGeneralizations of Borel-Cantelli Lemma
The Borel-Cantelli Lemma is very important in the probability theory. In this paper, we first describe the general case of the Borel-Cantelli Lemma. The first part of this lemma, assuming convergence and the second part includes divergence and independence assumptions. In the following, we have brought generalizations of the first and second part of this lemma. In most generalizat...
متن کاملThe 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 کاملBorel completeness of some א0-stable theories
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.
متن کاملThe residual spectrum of $U(n,n)$; contribution from Borel subgroups
In this paper we study the residual spectrum of the quasi-split unitary group $G=U(n,n)$ defined over a number field $F$, coming from the Borel subgroups, $L_{dis}^2(G(F)backslash G(Bbb A))_T$. Due to lack of information on the local results, that is, the image of the local intertwining operators of the principal series, our results are incomplete. However, we describe a conjec...
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:
- J. Symb. Log.
دوره 76 شماره
صفحات -
تاریخ انتشار 2011