scholarly journals Borel complexity and potential canonical Scott sentences

2017 ◽  
Vol 239 (2) ◽  
pp. 101-147 ◽  
Author(s):  
Douglas Ulrich ◽  
Richard Rast ◽  
Michael C. Laskowski
Keyword(s):  
Borel Complexity ◽  
Scott Sentences

scholarly journals The Borel complexity of von Neumann equivalence

2020 ◽  
pp. 102913
Author(s):  
Inessa Moroz ◽  
Asger Törnquist
Keyword(s):  
Von Neumann ◽  
Borel Complexity

scholarly journals THE CLASSIFICATION PROBLEM FOR AUTOMORPHISMS OF C*-ALGEBRAS

2015 ◽  
Vol 21 (4) ◽  
pp. 402-424 ◽  
Author(s):  
MARTINO LUPINI
Keyword(s):  
Complexity Theory ◽  
Classification Problem ◽  
C Algebras ◽  
Borel Complexity ◽  
Recent Developments

AbstractWe present an overview of the recent developments in the study of the classification problem for automorphisms of C*-algebras from the perspective of Borel complexity theory.

Why some people are excited by Vaught's conjecture

1985 ◽  
Vol 50 (4) ◽  
pp. 973-982 ◽  
Author(s):  
Daniel Lascar
Keyword(s):  
Model Theory ◽  
Continuum Hypothesis ◽  
Complete Theory ◽  
Scott Sentences ◽  
Countable Theory ◽  
The Continuum ◽  
Countable Models

§I. In 1961, R. L. Vaught ([V]) asked if one could prove, without the continuum hypothesis, that there exists a countable complete theory with exactly ℵ1 isomorphism types of countable models. The following statement is known as Vaught conjecture:Let T be a countable theory. If T has uncountably many countable models, then T hascountable models.More than twenty years later, this question is still open. Many papers have been written on the question: see for example [HM], [M1], [M2] and [St]. In the opinion of many people, it is a major problem in model theory.Of course, I cannot say what Vaught had in mind when he asked the question. I just want to explain here what meaning I personally see to this problem. In particular, I will not speak about the topological Vaught conjecture, which is quite another issue.I suppose that the first question I shall have to face is the following: “Why on earth are you interested in the number of countable models—particularly since the whole question disappears if we assume the continuum hypothesis?” The answer is simply that I am not interested in the number of countable models, nor in the number of models in any cardinality, as a matter of fact. An explanation is due here; it will be a little technical and it will rest upon two names: Scott (sentences) and Morley (theorem).

scholarly journals Hanf number for Scott sentences of computable structures

2018 ◽  
Vol 57 (7-8) ◽  
pp. 889-907
Author(s):  
S. S. Goncharov ◽  
J. F. Knight ◽  
I. Souldatos
Keyword(s):  
Computable Structures ◽  
Hanf Number ◽  
Scott Sentences

scholarly journals Scott sentences for certain groups

2017 ◽  
Vol 57 (3-4) ◽  
pp. 453-472 ◽  
Author(s):  
Julia F. Knight ◽  
Vikram Saraph
Keyword(s):  
Scott Sentences

scholarly journals Games with winning conditions of high Borel complexity

2006 ◽  
Vol 350 (2-3) ◽  
pp. 345-372 ◽  
Author(s):  
Olivier Serre
Keyword(s):  
Borel Complexity

Measure Convex and Measure Extremal Sets

2006 ◽  
Vol 49 (4) ◽  
pp. 536-548 ◽  
Author(s):  
Petr Dostál ◽  
Jaroslav Lukeš ◽  
Jiří Spurný
Keyword(s):  
Convex Sets ◽  
Borel Complexity ◽  
Extremal Sets ◽  
Positive Results

AbstractWe prove that convex sets are measure convex and extremal sets are measure extremal provided they are of low Borel complexity. We also present examples showing that the positive results cannot be strengthened.

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