منابع مشابه
Borel structures and Borel theories
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 be...
متن کاملBorel Structures: a Brief Survey
We survey some research aiming at a theory of effective structures of size the continuum. The main notion is the one of a Borel presentation, where the domain, equality and further relations and functions are Borel. We include the case of uncountable languages where the signature is Borel. We discuss the main open questions in the area.
متن کاملOn the Reductive Borel-serre Compactification, Iii: Mixed Hodge Structures
We establish a procedure for constructing compatible mixed Hodge structures for the cohomology of various topological compactifications of locally symmetric varieties, notably ones that are not algebraic varieties. This is carried out in full for the case of the reductive Borel-Serre compactification, and conditionally for the excentric compactifications. Introduction. In [BS], Borel and Serre ...
متن کاملOn Modified Borel Methods
for x>0. One says that 5-lim 5„ = 5|7?'-lim 5„ = 5] if lim^.,*, B(x; sk) = s[limx^x B'(x; sk)=s]. The relations between these Borel methods B, B', and their behavior under change of index are known [8, p. 183; 6; 7]. Following a suggestion of R. P. Boas, Jr., we intend to study in this paper the modified Borel methods which arise when the continuous variable x in (1.1) is replaced by the discre...
متن کاملNotes on Borel Determinacy
In this talk, we will provide a high level sketch of Martin’s proof of Borel Determinacy.
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1970
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-21-2-199-204