共查询到20条相似文献,搜索用时 46 毫秒
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2.
Yu. L. Ershov 《Algebra and Logic》2006,45(1):26-48
It is proved that the principal sublattice of a Rogers semilattice of a finite partially ordered set is definable. For this
goal to be met, we present a generalization of the Denisov theorem concerning extensions of embeddings of Lachlan semilattices
to ideals of Rogers semilattices. 相似文献
3.
S. Yu. Podzorov 《Siberian Advances in Mathematics》2007,17(3):171-185
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 Σ 3 0 -representation as an algebra but need not be a Lachlan semilattice if it admits a Σ 3 0 -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 Δ 2 0 -representation is positive. 相似文献
4.
A. M. Sokolovskaya 《Mathematical Notes》2007,82(5-6):827-835
We suggest a method for constructing G-spaces X such that the semilattice of G-compactifications of X coincides with the disjoint union of two semilattices corresponding to partitions of X into subspaces in which the maximal elements are identified. This method is applied to construct examples of G-Tychonoff spaces for which the semilattices of equivariant compactifications are of fairly simple structure and contain elements which are minimal but not least. 相似文献
5.
Sergio A. Celani 《Central European Journal of Mathematics》2003,1(4):561-572
In this paper we shall give a topological representation for Hilbert algebras that extend the topological representation given
by A. Diego in [4]. For implicative semilattices this representation gives a full duality. We shall also consider the representation
for Boolean ring. 相似文献
6.
N. Tsinaridze 《Journal of Mathematical Sciences》2013,191(6):871-875
We give a complete classification of all XI-subsemilattices of the semilattice of the class Σ2(X, 8). We derive formulas for calculating the numbers of semilattices of the given class. 相似文献
7.
Ivan Chajda 《Discrete Mathematics》2007,307(1):115-118
We present a simple equational characterization of (meet) semilattices with 0 where for each element p the interval [0,p] is an orthomodular lattice or an ortholattice possibly satisfying the compatibility condition. 相似文献
8.
S. Yu. Podzorov 《Algebra and Logic》2005,44(2):82-94
We deal in specific features of the algebraic structure of Rogers semilattices of n
0-computable numberings, for n 2. It is proved that any Lachlan semilattice is embeddable (as an ideal) in such every semilattice, and that over an arbitrary non 0-principal element of such a lattice, any Lachlan semilattice is embeddable (as an interval) in it.Supported by INTAS grant No. 00-499, by FP Universities of Russia grant UR.04.01.013, and by the Grant Center for Fundamental Research (GCFR), project PD02-1.1-475.__________Translated from Algebra i Logika, Vol. 44, No. 2, pp. 148–172, March–April, 2005. 相似文献
9.
We introduce a general technique for finding sets of axioms for a given class of semigroups. To illustrate the technique, we provide new sets of defining axioms for groups of exponent n, bands, and semilattices. 相似文献
10.
Ulrich Heckmanns 《Results in Mathematics》1999,36(3-4):260-270
We determine the injective objects and hulls in the category POSV. This category is similar to the one of join semilattices but contains all partially ordered sets. The results of this paper have applications, for instance, in the theory of (generalized) ultrametric spaces. 相似文献
11.
We define geometric semilattices, a generalization of geometric lattices. The poset of independent sets of a matroid is another example. We prove several axiomatic and constructive characterizations, for example: geometric semilattices are those semilattices obtained by removing a principal filter from a geometric lattice. We also show that all geometric semilattices are shellable, unifying and extending several previous results.Partially supported by NSF grant MCS 81-03474. 相似文献
12.
A. I. Stukachev 《Siberian Advances in Mathematics》2010,20(1):68-74
We prove an analogue of the jump inversion theorem for the semilattices of Σ-degrees of structures. As a corollary, we get
a similar result for the semilattices of degrees of presentability of countable structures. 相似文献
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14.
M. V. Lawson 《Semigroup Forum》2010,81(1):187-199
We characterize those semilattices that give rise to Boolean spaces on their associated spaces of ultrafilters. The class
of 0-disjunctive semilattices, important in the theory of congruence-free inverse semigroups, plays a distinguished role in
this theory. 相似文献
15.
Characterizations are given of semigroupsS for which everyS-system is tree ordered and semigroupsS for which everyS-system is a free sum of tree semilattices. 相似文献
16.
Jan Paseka 《Order》2008,25(1):69-77
We introduce semilattices equipped with a partial n-ary operation ρ. A useful separation lemma for such nontrivial complete partial ρ-semilattices is proved equivalent to PIT, the prime ideal theorem. The relation of various versions of the Lemma to each other and to PIT is also explored.
Supported by the Ministry of Education of the Czech Republic under the project MSM0021622409. 相似文献
17.
Hisato Muraki 《Mathematical Logic Quarterly》1997,43(3):378-388
In this note, we study the complementedness and the distributivity of upper semilattices of Kleene degrees assuming V = L. K denotes the upper semilattice of all Kleene degrees. We prove that if V = L, then some sub upper semilattices of K are non-complemented and some are non-distributive. 相似文献
18.
O. Givradze 《Journal of Mathematical Sciences》2012,186(5):745-750
In complete semigroups of unions B x (D) defined by semilattices of class ??2(X, 4), we selecte subsets of certain type on which equivalent binary relations are defined and by means of these relations, irreducible generating sets of the considered semigroups are described. 相似文献
19.
In this note we characterize weakly self-injective semilattices as Brouwerian semilattices which are compact in the residuated
interval topology. We also characterize weakly self-injective semigroups which are semilattices of groups with trivial multiplication.
Research of first author supported in part by a research grant from the Faculty Research Committee of Bowling Green State
University.
Research of second author supported in part by a postdoctoral fellowship in the Biomathematics Program at North Carolina State
University under PHS Grant #GM-678 from NIGMS. 相似文献
20.
Miroslav Ploščica 《Algebra Universalis》2005,54(3):323-335
We introduce the Local Separation Property (LSP) for distributive semilattices. We show that LSP holds in many semilattices
of the form Conc A, where A is a lattice. On the other hand, we construct an abstract example of a distributive lattice without LSP. Our research is
connected with the well known open problem whether every distributive algebraic lattice is isomorphic to the congruence lattice
of some lattice.
Received December 10, 2004; accepted in final form June 6, 2005. 相似文献