sergei badaev - Academia.edu (original) (raw)

Uploads

Papers by sergei badaev

Algebra and Logic, 2001

We look into algebraic properties of Rogers semilattices of arithmetic sets, such as the existenc... more We look into algebraic properties of Rogers semilattices of arithmetic sets, such as the existence of minimal elements, minimal covers, and ideals without minimal elements.

Siberian Mathematical Journal, 2008

We present some examples and constructions in the theory of complete numberings and completions o... more We present some examples and constructions in the theory of complete numberings and completions of numberings that partially answer a few questions of [1].

We investigate differences in the elementary theories of Rogers semilattices of arithmetical numb... more We investigate differences in the elementary theories of Rogers semilattices of arithmetical numberings, depending on structural invariants of the given families of arithmetical sets. It is shown that at any fixed level of the arithmetical hierarchy there exist infinitely many families with pairwise elementary different Rogers semilattices.

We investigate differences in the isomorphism types of Rogers semilattices of computable numberin... more We investigate differences in the isomorphism types of Rogers semilattices of computable numberings of families of sets lying in different levels of the arithmetical hierarchy.

Algebra and Logic, 2005

It is proved that for every level of the arithmetic hierarchy, there exist infinitely many famili... more It is proved that for every level of the arithmetic hierarchy, there exist infinitely many families of sets with pairwise non-elementarily equivalent Rogers semilattices.

Algebra and Logic, 1998

We are concerned with Ershov’s problem of obtaining a characterization of families with one-eleme... more We are concerned with Ershov’s problem of obtaining a characterization of families with one-element Rogers semilattice (the semilattice of computable enumerations of a family). An algorithmic description is furnished for the families of recursive functions whose Rogers semilattice is one-element. It is proved that there exists a nontrivial family of recursively enumerable sets with the least set under inclusion, whose Rogers semilattice consists of a single element.

Algebra and Logic, 2006

We investigate differences in isomorphism types for Rogers semilattices of computable numberings ... more We investigate differences in isomorphism types for Rogers semilattices of computable numberings of families of sets lying in different levels of the arithmetical hierarchy.

Algebra and Logic, 2001

We look into algebraic properties of Rogers semilattices of arithmetic sets, such as the existenc... more We look into algebraic properties of Rogers semilattices of arithmetic sets, such as the existence of minimal elements, minimal covers, and ideals without minimal elements.

Siberian Mathematical Journal, 2008

We present some examples and constructions in the theory of complete numberings and completions o... more We present some examples and constructions in the theory of complete numberings and completions of numberings that partially answer a few questions of [1].

We investigate differences in the elementary theories of Rogers semilattices of arithmetical numb... more We investigate differences in the elementary theories of Rogers semilattices of arithmetical numberings, depending on structural invariants of the given families of arithmetical sets. It is shown that at any fixed level of the arithmetical hierarchy there exist infinitely many families with pairwise elementary different Rogers semilattices.

We investigate differences in the isomorphism types of Rogers semilattices of computable numberin... more We investigate differences in the isomorphism types of Rogers semilattices of computable numberings of families of sets lying in different levels of the arithmetical hierarchy.

Algebra and Logic, 2005

It is proved that for every level of the arithmetic hierarchy, there exist infinitely many famili... more It is proved that for every level of the arithmetic hierarchy, there exist infinitely many families of sets with pairwise non-elementarily equivalent Rogers semilattices.

Algebra and Logic, 1998

We are concerned with Ershov’s problem of obtaining a characterization of families with one-eleme... more We are concerned with Ershov’s problem of obtaining a characterization of families with one-element Rogers semilattice (the semilattice of computable enumerations of a family). An algorithmic description is furnished for the families of recursive functions whose Rogers semilattice is one-element. It is proved that there exists a nontrivial family of recursively enumerable sets with the least set under inclusion, whose Rogers semilattice consists of a single element.

Algebra and Logic, 2006

We investigate differences in isomorphism types for Rogers semilattices of computable numberings ... more We investigate differences in isomorphism types for Rogers semilattices of computable numberings of families of sets lying in different levels of the arithmetical hierarchy.

Log In