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A semilattice of numberings. II. (English. Russian original) Zbl 1262.03074
Algebra Logic 49, No. 4, 340-353 (2010); translation from Algebra Logika 49, No. 4, 498-519 (2010).
Summary: \(\mathfrak{c}\)-universal semilattices \(\mathfrak{A}\) of the power of the continuum (of an upper semilattice of \(m\)-degrees) on admissible sets are studied. Moreover, it is shown that a semilattice of \(\mathbb{H}\mathbb{F}(\mathfrak{M})\)-numberings of a finite set is \(\mathfrak{c}\)-universal if \(\mathfrak{M}\) is a countable model of a \(c\)-simple theory.
For Part I see [Mat. Tr. 12, No. 2, 170–209 (2009); translation in Sib. Adv. Math. 20, No. 2, 128–154 (2010; Zbl 1249.03086)].

MSC:
03D60 Computability and recursion theory on ordinals, admissible sets, etc.
03C57 Computable structure theory, computable model theory
03D25 Recursively (computably) enumerable sets and degrees
03D30 Other degrees and reducibilities in computability and recursion theory
03D45 Theory of numerations, effectively presented structures
06A12 Semilattices
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References:
[1] Yu. L. Ershov, Numeration Theory [in Russian], Nauka, Moscow (1977).
[2] V. G. Puzarenko, ”A semilattice of numberings,” Mat. Tr., 12, No. 2, 170–209 (2009). · Zbl 1249.03086
[3] H. Rogers, Theory of Recursive Functions and Effective Computability, McGraw-Hill, New York (1967). · Zbl 0183.01401
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[6] J. Barwise, Admissible Sets and Structures, Springer, Berlin (1975). · Zbl 0316.02047
[7] V. G. Puzarenko, ”Computability over models of decidable theories,” Algebra Logika, 39, No. 2, 170–197 (2000). · Zbl 0954.03044
[8] V. G. Puzarenko, ”Generalized numberings and the definability of a field $$ \(\backslash\)mathbb{R} $$ in admissible sets,” Vestnik NGU, Mat., Mekh., Inf., 3, No. 2, 107–117 (2003). · Zbl 1033.03029
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