Elementary Theories for Rogers Semilattices

It is proved that for every level of the arithmetic hierarchy, there exist infinitely many families of sets with pairwise non-elementarily equivalent Rogers semilattices.Supported by INTAS grant No. 00-499.__________Translated from Algebra i Logika, Vol. 44, No. 3, pp. 261–268, May–June, 2005.     

P-完全正则半群

求证具有强半格结构的完全正则半群成为P-完全正则半群的充分条件.利用半群的强半格结构以及同余的性质.完全单半群的强半格-正规群带是P-完全正则半群.矩形群的强半格正规纯正群类ONBG,左群的强半格左正规纯整群类LONBG,群的强半格Clifford半群类,矩形带的强半格正规带类NB,都具有性质P.     

SOME REMARKS ON （L）-GREEN’S RELATIONS AND STRONGLY RPP SEMIGROUPS

In order to study rpp semigroups, in particular, some special cases, several facts on (l)-Green’s relations and strongly rpp semigroups are given as some remarks.     

On Ordered Semigroups Which are Semilattices of Simple and Regular Semigroups

We characterize the ordered semigroups which are decomposable into simple and regular components. We prove that each ordered semigroup which is both regular and intra-regular is decomposable into simple and regular semigroups, and the converse statement also holds. We also prove that an ordered semigroup S is both regular and intra-regular if and only if every bi-ideal of S is an intra-regular (resp. semisimple) subsemigroup of S. An ordered semigroup S is both regular and intra-regular if and only if the left (resp. right) ideals of S are right (resp. left) quasi-regular subsemigroups of S. We characterize the chains of simple and regular semigroups, and we prove that S is a complete semilattice of simple and regular semigroups if and only if S is a semilattice of simple and regular semigroups. While a semigroup which is both π-regular and intra-regular is a semilattice of simple and regular semigroups, this does not hold in ordered semigroups, in general.     

On transitive Cayley graphs of strong semilattices of right (left) groups

We investigate Cayley graphs of strong semilattices of right (left) groups, of right (left) zero semigroups, and of groups. We show under which conditions they enjoy the property of automorphism vertex transitivity in analogy to Cayley graphs of groups.     

可数Scott闭集格

讨论可数定向偏序集P上的Cσ(P)的一些性质。主要结果有:(1)每个Cσ(P)都是可数C-连续的;(2)完备格M与Cσ(其中P是可数定向完备半格)同构当且仅当M为弱-可数稳定C-代数格;(3)设P,Q为可数定向完备偏序集,f:P→Q是可数Scott连续映射,h:Cσ(P)→Cσ(Q)为f-1的下伴随,则h保c关系。更多还原     

Ideals of Priestley powers of semilattices

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.     

Recursively Enumerable Equivalence Relations Modulo Finite Differences

We investigate the upper semilattice Eq* of recursively enumerable equivalence relations modulo finite differences. Several natural subclasses are shown to be first-order definable in Eq*. Building on this we define a copy of the structure of recursively enumerable many-one degrees in Eq*, thereby showing that Th(Eq*) has the same computational complexity as the true first-order arithmetic. Mathematics Subject Classification: 03D25, 03D15, 03D35.