This article is cited in 4 scientific papers (total in 4 papers)
Numbered Distributive Semilattices
S. Yu. Podzorov
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
In this article, we consider several definitions of a Lachlan semilattice; i. e., a semilattice isomorphic to a principal ideal of the semilattice of computably enumerable $m$-degrees. We also answer a series of questions on constructive posets and prove that each distributive semilattice with top and bottom is a Lachlan semilattice if it admits a $\Sigma^0_3$-representation as an algebra but need not be a Lachlan semilattice if it admits a $\Sigma^0_3$-representation as a poset. The examples are constructed of distributive lattices that are constructivizable as posets but not constructivizable as join (meet) semilattices. We also prove that every locally lattice poset (in particular, every lattice and every distributive semilattice) possessing a $\Delta^0_2$-representation is positive.
distributive lattice, distributive semilattice, numbering, constructivization, positive structure, Lachlan semilattice.
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Siberian Advances in Mathematics, 2007, 17:3, 171–185
S. Yu. Podzorov, “Numbered Distributive Semilattices”, Mat. Tr., 9:2 (2006), 109–132; Siberian Adv. Math., 17:3 (2007), 171–185
Citation in format AMSBIB
\paper Numbered Distributive Semilattices
\jour Mat. Tr.
\jour Siberian Adv. Math.
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This publication is cited in the following articles:
S. Yu. Podzorov, “The universal Lachlan semilattice without the greatest element”, Algebra and Logic, 46:3 (2007), 163–187
S. Yu. Podzorov, “Arithmetical $D$-degrees”, Siberian Math. J., 49:6 (2008), 1109–1123
Podzorov S., “Upper semilattices in many-one degrees”, Logic and Theory of Algorithms, Lecture Notes in Computer Science, 5028, 2008, 491–497
J. Wallbaum, “A $\Delta^0_2$-poset with no positive presentation”, Algebra and Logic, 51:4 (2012), 281–284
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