Morozov, A. S. Presentability of groups of \(\Sigma\)-definable permutations over admissible sets. (Russian, English) Zbl 1016.03042 Algebra Logika 41, No. 4, 459-480 (2002); translation in Algebra Logic 41, No. 4, 254-266 (2002). The author examines possibilities for generalizing the well-known Nurtazin result that the group of all computable permutations of natural numbers is not isomorphic to a constructive group. It is proven that the group of all \(\Sigma\)-permutations of an arbitrary locally countable, recursively listed, admissible set is not \(\Sigma\)-presentable over the set. An example is constructed showing that this group can be presentable provided that the local countability condition is dropped. Reviewer: A.N.Ryaskin (Novosibirsk) Cited in 1 Document MSC: 03D60 Computability and recursion theory on ordinals, admissible sets, etc. 03C57 Computable structure theory, computable model theory 20A15 Applications of logic to group theory Keywords:group of \(\Sigma\)-permutations; \(\Sigma \)-definable permutation; \(\Sigma \)-presentable permutation; \(\Sigma \)-definability; locally countable, recursively listed, admissible set PDFBibTeX XMLCite \textit{A. S. Morozov}, Algebra Logika 41, No. 4, 459--480 (2002; Zbl 1016.03042); translation in Algebra Logic 41, No. 4, 254--266 (2002) Full Text: EuDML