an:06114998
Zbl 1262.03074
Puzarenko, V. G.
A semilattice of numberings. II
EN
Algebra Logic 49, No. 4, 340-353 (2010); translation from Algebra Logika 49, No. 4, 498-519 (2010).
0002-5232 1573-8302
2010
j
03D60 03C57 03D25 03D30 03D45 06A12
computably enumerable set; admissible set; \(\mathbb{A}\)-numbering; \(m\Sigma\)-reducibility; hereditarily finite superstructure; natural ordinal; upper semilattice; \(\mathfrak{c}\)-universal semilattice
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)].
1249.03086