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Subjects
03-XX Mathematical logic and foundations
03Dxx Computability and recursion theory
03D45 Theory of numerations, effectively presented structures

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The concept of a binary relation over partial enumerated sets.

Algebra i Logika

The degree spectra of definable relations on Boolean algebras.

Semukhin, P.M. (2005)

Sibirskij Matematicheskij Zhurnal

The effective Borel hierarchy

M. Vanden Boom (2007)

Fundamenta Mathematicae

Let K be a subclass of Mod() which is closed under isomorphism. Vaught showed that K is $Σ_{α}$ (respectively, $Π_{α}$ ) in the Borel hierarchy iff K is axiomatized by an infinitary $Σ_{α}$ (respectively, $Π_{α}$ ) sentence. We prove a generalization of Vaught’s theorem for the effective Borel hierarchy, i.e. the Borel sets formed by union and complementation over c.e. sets. This result says that we can axiomatize an effective $Σ_{α}$ or effective $Π_{α}$ Borel set with a computable infinitary sentence of the same complexity. This result...

Torsion-free constructive nilpotent $R_{p}$ -groups.

Khisamiev, N.G. (2009)