The Friedman embedding theorem.

DOI10.1016/j.jalgebra.2011.02.033zbMath1233.20030OpenAlexW2005609978MaRDI QIDQ645257

Simon Thomas

Publication date: 8 November 2011

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2011.02.033

zbMATH Keywords

Borel equivalence relationscombinatorial group theorycountable groupsrecursion theory2-generator groupsTuring degreesHigman-Neumann-Neumann embedding theoremHigman-Neumann-Neumann extensions

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Generators, relations, and presentations of groups (20F05) Descriptive set theory (03E15) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Word problems, etc. in computability and recursion theory (03D40)

Cites Work

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• Borel determinacy
• On the complexity of the isomorphism relation for finitely generated groups
• The space of finitely generated groups
• Embeddings into hopfian groups
• A remark on the Higman–Neumann–Neumann embedding theorem
• DEGREES OF GROWTH OF FINITELY GENERATED GROUPS, AND THE THEORY OF INVARIANT MEANS
• Embedding Countable Groups in 2-Generator Groups
• The axiom of determinateness and reduction principles in the analytical hierarchy
• Embedding Theorems for Groups
• Borel equivalence relations and classifications of countable models

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