ScholarLens Back to search
2011•Journal of Symbolic LogicRequires access

Borel structures and Borel theories

Greg Hjorth, André Nies

Open publisher page 5 citations

Abstract

Abstract 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 uniformly Borel. We also investigate Borel isomorphisms between Borel structures.

About this research paper

What this paper is about

Abstract 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 uniformly Borel. We also investigate Borel isomorphisms between Borel structures.

Why it matters

OpenAlex reports 5 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Abstract 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 uniformly Borel. We also investigate Borel isomorphisms between Borel structures.

Key concepts: Borel equivalence relation, Borel hierarchy, Mathematics, Borel set, Equivalence relation, Borel measure, Pure mathematics, Equivalence (formal languages)

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
Borel structures and Borel theories — Research Paper | ScholarLens