The concept of a binary relation over partial enumerated sets.
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Algebra i Logika
Semukhin, P.M. (2005)
Sibirskij Matematicheskij Zhurnal
M. Vanden Boom (2007)
Fundamenta Mathematicae
Let K be a subclass of Mod() which is closed under isomorphism. Vaught showed that K is (respectively, ) in the Borel hierarchy iff K is axiomatized by an infinitary (respectively, ) 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 or effective Borel set with a computable infinitary sentence of the same complexity. This result...
Khisamiev, N.G. (2009)
Sibirskij Matematicheskij Zhurnal
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