The problem of solvability of a positive theory of an arbitrary group is algorithmically unsolvable

DOI10.22405/2226-8383-2023-24-1-40-49MaRDI QIDQ6194082

V. G. Durnev, A. I. Zetkina

Publication date: 14 February 2024

Published in: Chebyshevskii Sbornik (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/cheb1281

zbMATH Keywords

grouppositive formulapositive theoryalgorithmic solvability

Mathematics Subject Classification ID

Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Abstract and axiomatic computability and recursion theory (03D75)

Cites Work

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• Recursive unsolvability of group theoretic problems
• Positive theories of free monoids
• Positive indistinguishability of algebraic systems, and completeness of positive theories
• Almost all free products of groups have the same positive theory
• On recognising Hopf groups
• Embeddings into hopfian groups
• \(\exists\)-free groups

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