The extension of embeddings problem for the recursively enumer-able degrees R = (R; <; 0;0 0) asks for given nite partially ordered sets P Q with least and greatest elements, whether every embedding of P into R can be extended to an embedding of Q into R. Many of the landmark theorems giving an algebraic insight into R assert either extension or nonextension of embeddings. We extend, strengthen...

in this paper, we introduce the concept of semihyperring $(r,+,cdot)$ together with a suitable partial order $le$. moreover, we introduce and study hyperideals in ordered semihyperrings. simple ordered semihyperrings are defined and its characterizations are obtained. finally, we study some properties of quasi-simple and $b$-simple ordered semihyperrings.

Vx = {yeP:xSy} is the principal filter generated by x. The filters on P are easily seen to be the open sets for a topology on P, and the increasing maps from P to another locally finite partially ordered set Q are precisely the continuous functions from P to Q [5]. For each filter V on P, let M(P9 V\ or simply M(V) when reference to P is understood, denote the free abelian group on V. For filte...

By combining accurate heat capacity and x-ray resonant scattering results we have resolved the long standing question regarding the nature of the quadrupolar ordered phases in UPd(3). The order parameter of the highest temperature quadrupolar phase has been uniquely determined to be antiphase Q{zx} in contrast to the previous conjecture of Q{x{2}-y{2}}. The azimuthal dependence of the x-ray sca...

We prove the following theorem: For a partially ordered set Q such that every countable subset has a strict upper bound, there is a forcing notion satisfying ccc such that, in the forcing model, there is a basis of the null ideal of the real line which is order-isomorphic to Q with respect to set-inclusion. This is a variation of Hechler’s classical result in the theory of forcing, and the stat...

First order phase transitions are easily described in terms of the competition between two phases (see e.g. [1]). Consider for definiteness a temperature driven phase transition between a disordered phase and a q-fold degenerate ordered phase of free energy fd(β) and fo(β). In order to use numerical methods, one needs to know the behavior of statistical averages in a finite volume, close to the...

We prove that the class of permutations generated by passing an ordered sequence 12 . . . n through a stack of depth 2 and an infinite stack in series is in bijection with an unambiguous context-free language, where a permutation of length n is encoded by a string of length 3n. It follows that the sequence counting the number of permutations of each length has an algebraic generating function. ...

We prove the following theorem: For a partially ordered set Q such that every countable subset has a strict upper bound, there is a forcing notion satisfying ccc such that, in the forcing model, there is a basis of the null ideal of the real line which is order-isomorphic to Q with respect to set-inclusion. This is a variation of Hechler’s classical result in the theory of forcing, and the stat...

Manganese tricyanomethanide, Mn[C(CN)3]2, crystallizes in an orthorhombic lattice consisting of two interpenetrating three-dimensional rutile-like networks. In each network, the tridentate C(CN)3 anion gives rise to superexchange interactions between the Mn ions (S = 5/2) that can be mapped onto the “row model” for partially frustrated triangular magnets. We present heat capacity measurements t...

Baer [1] observed that modular lattices of finite length (for example subgroup lattices of abelian groups) can be conceived as subspace lattices of a projective geometry structure on an ordered point set; the set of join irreducibles which in this case are the cyclic subgroups of prime power order. That modular lattices of finite length can be recaptured from the order on the points and, in add...