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Том 56, № 3 (2017)
- Год: 2017
- Статей: 8
- URL: https://journals.rcsi.science/0002-5232/issue/view/14543
Article
Irreducible, Singular, and Contiguous Degrees
Аннотация
We study structures of degrees of stronger algorithmic reducibilities inside the degrees of weaker algorithmic ones. Results in this area are reviewed for algorithmic reducibilities m-, 1-, tt-, wtt-, T-, e-, s-, Q-, and we formulate questions that are still not settled for these. A computably enumerable Q-degree which consists of one computably enumerable m-degree is constructed.
181-196
The Isomorphism Problem for Generalized Baumslag–Solitar Groups with One Mobile Edge
Аннотация
A generalized Baumslag–Solitar group (GBS group) is a finitely generated group G which acts on a tree with all edge and vertex stabilizers infinite cyclic. Every GBS group is the fundamental group π1(????) of some labeled graph ????. This paper deals with the isomorphism problem for GBS groups, which is the problem of determining whether π1(????) ≅ π1(????) for two given labeled graphs ???? and ????. We describe an algorithm that decides this problem for the case where one of the labeled graphs has a sole mobile edge.
197-209
Constants of Partial Derivations and Primitive Operations
Аннотация
We describe algebras of constants of the set of all partial derivations in free algebras of unitarily closed varieties over a field of characteristic 0. These constants are also called proper polynomials. It is proved that a subalgebra of proper polynomials coincides with the subalgebra generated by values of commutators and Umirbaev–Shestakov primitive elements pm,n on a set of generators for a free algebra. The space of primitive elements is a linear algebraic system over a signature Σ = {[x, y], pm,n | m, n ≥ 1}. We point out bases of operations of the set Σ in the classes of all algebras, all commutative algebras, right alternative and Jordan algebras.
210-231
Generic Gӧdel’s Incompleteness Theorem
Аннотация
Gӧdel’s incompleteness theorem asserts that if formal arithmetic is consistent then there exists an arithmetic statement such that neither the statement nor its negation can be deduced from the axioms of formal arithmetic. Previously [3], it was proved that formal arithmetic remains incomplete if, instead of the set of all arithmetic statements, we consider any set of some class of “almost all” statements (the class of so-called strongly generic subsets). This result is strengthened as follows: formal arithmetic is incomplete for any generic subset of arithmetic statements (i.e., a subset of asymptotic density 1).
232-235
Decompositions in Complete Lattices II. Replaceable Irredundant Decompositions
Аннотация
A characterization of lattices with replaceable irredundant decompositions is given in the following six classes: the class of upper and lower continuous lattices; the class of upper continuous completely join-semidistributive lattices; the class of upper semimodular lower continuous lattices; the class of upper semimodular completely joinsemidistributive lattices; the class of consistent lower continuous lattices; the class of consistent completely join-semidistributive lattices.
236-244
Solvability of Equations in Classes of Solvable Groups and Lie Algebras
251-255
Sessions of the Seminar “Algebra i Logika”
256-259
Communications
Recognizable and Perceptible Logics and Varieties
245-250