Considering a commutative unital quantale L as the truth value table and using the tool of L-generalized convergence structures of stratified L-filters, this paper introduces a kind of fuzzy upper topology, called fuzzy S-upper topology, on L-preordered sets. It is shown that every fuzzy join-preserving L-subset is open in this topology. When L is a complete Heyting algebra, for every completel...

We present transformations of linearly ordered sets into ordered abelian groups and ordered fields. We study effective properties of the transformations. In particular, we show that a linear order L has a ∆2 copy if and only if the corresponding ordered group (ordered field) has a computable copy. We apply these codings to study the effective categoricity of linear ordered groups and fields.

In this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. Also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. Furthermore,...

Let A ⊆ [n] × [n] be a set of pairs containing the diagonal D = {(i, i) | i = 1, . . . , n}, and such that a ≤ b for all (a, b) ∈ A. We study formulae for the generating series FA(x) = ∑ w x w where the sum is over all words w ∈ [n]∗ that avoid A, i.e., (wi, wi+1) 6∈ A for i = 1, . . . , |w| − 1. This series is a rational function, with denominator of the form 1−∑T μA(T )xT , where the sum is o...

employing the notions of the strong $l$-topology introduced by zhangand the $l$-frame introduced by yao  and the concept of $l$-enrichedtopological system defined in the present paper, we constructadjunctions among the categories {bf st$l$-top} of strong$l$-topological spaces, {bf s$l$-loc} of strict $l$-locales and{bf $l$-entopsys} of $l$-enriched topological systems. all of theseconcepts are ...

In a paper entitled Noncommutative valuations, Schilling [8] proved that if an algebra of finite order over its center is relatively complete in a valuation (where the value group of the nonarchimedean, exponential valuation is not assumed to be commutative) then the value group is commutative. A similar type of theorem, proved by Albert [l], states that if an algebra of finite order over a fie...