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Let be a Δ 1 1 -constructivizable model. If its Scott rank is strictly less than ω 1 CK , then it is proved autostable. But if , then there exists an ordinal α<ω 1 CK for which is not autostable in any degree O (γ+1) for all γ>α. We also consider some problems concerning Δ 1 1...
Every group that is finitely presented in the variety A n of solvable groups. and is universally equivalent to a free group F r ( A n ) in this variety, is embedded in the Cartesian degree of F 2 ( A n ). All subgroups on a set of two generators in that Cartesian degree which are universally...
Independent bases of admissible inference rules are studied; namely, we treat inference rules in pretable modal logics over S4, and in pretable superintuitionistic logics. The Maksimova-Esakia-Meskhi theorem holds that there exist exactly five pretable S4-logics and precisely three pretable...
We prove the quantifier-elimination theorem for so-called primitive connected theories, exemplified by theories of modules. The theorem generalizes the well-known Baur-Monk-Garavaglia theorem on the elimination of quantifiers in the model theory of modules. The definition of a class of primitive...
Σ-definability in hereditarily finite superstructures over algebraic systems is studied. We prove the Σ-definability criterion, which is then used as a basis for establishing the reduction theorem for regular theories and for obtaining a characterization of simple theories. The idea of a...
We construct a two-generated group with the co-recursively enumerable word problem that has no presentation by recursive permutations. This answers Higman’s question and exemplifies a group with the minimal possible number of generators. The previous article (1), in which that question was...
For any natural k ≥ 3 and l ≥ 2, we describe decidability boundaries for two varieties: the variety of all k-nilpotent groups and the variety of all l-solvable groups.
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