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S. Yu. Podzorov 《Algebra and Logic》2007,46(3):163-187
We deal with some upper semilattices of m-degrees and of numberings of finite families. It is proved that the semilattice
of all c.e. m-degrees, from which the greatest element is removed, is isomorphic to the semilattice of simple m-degrees, the
semilattice of hypersimple m-degrees, and the semilattice of Σ
2
0
-computable numberings of a finite family of Σ
2
0
-sets, which contains more than one element and does not contain elements that are comparable w.r.t. inclusion.
Supported by the Grant Council (under RF President) for Young Russian Scientists via project MK-1820.2005.1.
__________
Translated from Algebra i Logika, Vol. 46, No. 3, pp. 299–345, May–June, 2007. 相似文献
3.
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
4.
We give a criterion for a linearly ordered topological semilattice to be H-closed. We also prove that any linearly ordered H-closed topological semilattice is absolutely H-closed and we show that every linearly ordered semilattice is a dense subsemilattice of an H-closed topological semilattice. 相似文献
5.
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
6.
The combinatorial simple principal ideal semigroups generated by two elements were described by L. Megyesi and G. Pollák.
The ‘most general’ among them is called the Rédei semigroup. The ‘most special’ combinatorial simple principal ideal semigroup
generated by two elements is the bicyclic semigroup. D. B. McAlister determined the compatible semilattice orders on the bicyclic
semigroup. Our aim is to study the compatible semilattice orders on the homomorphic images of the Rédei semigroup. We prove
that there are four compatible total orders on these semigroups. We show that on the Rédei semigroup, the total orders are
the only compatible semilattice orders. Moreover, on each proper homomorphic image of the Rédei semigroup, we give a compatible
semilattice order which is not a total order.
Communicated by Mária B. Szendrei 相似文献
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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
9.
在序半群上定义了几种新的关系,利用它们得到了序半群上最小完全半素理想的结构,并以此给出了序半群的最小正则半格同余的另一种描述,所得结果是Miroslav Ciric在文[1]中的部分结果向序半群上的推广。 相似文献
10.
§1.m┐semilaticesGivenacardinalm.AposetPiscaledanm-semilatice,ifforanynon-emptysubsetBofPwith|B|<m,theinfimum∧BexistsinP.Asetw... 相似文献
11.
AN INVARIANT FOR HYPERGRAPHS 总被引:11,自引:0,他引:11
ANINVARIANTFORHYPERGRAPHSWANGJIANFANG(InstituteofAPPliedMathematics,ChineseAcademyofSciences,Beijing100080,ChinaandAsia-Pacif... 相似文献
12.
利用自由含幺半群X*上的一个偏序关系,介绍了一类特殊的后缀码.通过定义这类后缀码上的两种二元运算,研究了这类后缀码的代数性质.证明了该子类在这两种运算下形成一个加法导出是半格的半环,并且满足吸收律.从而提供了一个满足吸收律的半格序半群的例子. 相似文献
13.
We investigate differences in isomorphism types for Rogers semilattices of computable numberings of families of sets lying
in different levels of the arithmetical hierarchy.
Supported by RFBR grant No. 05-01-00819 and by INTAS grant No. 00-499.
Supported by NSFC grant No. 60310213.
__________
Translated from Algebra i Logika, Vol. 45, No. 6, pp. 637–654, November–December, 2006. 相似文献
14.
We generalize the concept of an integral residuated lattice to join-semilattices with an upper bound where every principal
order-filter (section) is a residuated semilattice; such a structure is called a sectionally residuated semilattice. Natural examples come from propositional logic. For instance, implication algebras (also known as Tarski algebras), which
are the algebraic models of the implication fragment of the classical logic, are sectionally residuated semilattices such
that every section is even a Boolean algebra. A similar situation rises in case of the Lukasiewicz multiple-valued logic where
sections are bounded commutative BCK-algebras, hence MV-algebras. Likewise, every integral residuated (semi)lattice is sectionally
residuated in a natural way. We show that sectionally residuated semilattices can be axiomatized as algebras (A, r, →, ⇝, 1) of type 〈3, 2, 2, 0〉 where (A, →, ⇝, 1) is a {→, ⇝, 1}-subreduct of an integral residuated lattice. We prove that every sectionally residuated lattice can be isomorphically embedded into a residuated lattice in which the ternary operation r is given by r(x, y, z) = (x · y) ∨ z. Finally, we describe mutual connections between involutive sectionally residuated semilattices and certain biresiduation
algebras.
This work was supported by the Czech Government via the project MSM6198959214. 相似文献
15.
Ideals of Priestley powers of semilattices 总被引:1,自引:0,他引:1
J. D. Farley 《Algebra Universalis》1999,41(4):239-254
Let X be a poset and Y an ordered space; X
Y
denotes the poset of continuous order-preserving maps from Y to X with the discrete (respectively, Scott, Lawson) topology. If S is a -semilattice, its ideal semilattice, and T a bounded distributive lattice with Priestley dual space P(T), it is shown that the following isomorphisms hold: Moreover, and sufficient conditions and necessary conditions for the isomorphism to hold are obtained (both necessary and sufficient
if S is a distributive -semilattice).
Received September 27, 1995; accepted in final form April 6, 1998. 相似文献
16.
Yu. L. Ershov 《Algebra and Logic》2003,42(4):232-236
We establish a condition that is necessary for Rogers semilattices of computable numberings of finite families of computably enumerable sets to be isomorphic. 相似文献
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Melis Minisker 《Semigroup Forum》2009,78(1):99-105
In this paper we consider certain ranks of some semigroups. These ranks are r
1(S),r
2(S),r
3(S),r
4(S) and r
5(S) as defined below. We have r
1≤r
2≤r
3≤r
4≤r
5. The semigroups are CL
n
,CL
m
×CL
n
,Z
n
and SL
n
. Here CL
n
is a chain with n elements, Z
n
is the zero semigroup on n elements and SL
n
is the free semilattice generated by n elements and having 2
n
−1 elements. We find many of the ranks for these classes of semigroups. 相似文献
20.
设含幺元的半群A是幺半群A~_e的半格,其中A的幺元为1_A,A~_e的幺元为e,所有幺元e的集合为E(A),则对于幺半群A上的Rees矩阵半群S和幺半群A~_e上的Rees矩阵半群S~_e,以下五个条件是等价的:(1)任意的e∈E(A),a∈A,有ae=ea;(2)A是幺半群A~_e的强半格;(3)S是S~_e的强半格;(4)A的平移壳和A~_e的平移壳的强半格同构;(5)S的平移壳和S~_e的平移壳的强半格同构. 相似文献