Generalizing the fact that Scott’s continuous lattices form the equational hull of the class of all algebraic lattices, we describe an equational hull of LFP, the category of locally finitely presentable categories, over CAT. Up to a set-theoretical hypothesis this hull is formed by the category of all precontinuous categories, i.e., categories in which limits and filtered colimits distribute. ...

A coalgebraic, equational approach to the speci(cation of observational structures allowing for a choice in the result type of observations is presented. Observers whose result type is structured as a coproduct of basic types are considered, and notions of covariable, coterm and coequation, dual to the algebraic notions of variable, term and equation are used to specify the associated structure...

This paper addresses some questions about the variety generated by the algebra of truth values of type-2 fuzzy sets. Its principal result is that this variety is generated by a nite algebra, and in particular is locally nite. This provides an algorithm for determining when an equation holds in this variety. It also sheds light on the question of determining an equational axiomatization of this ...

Commutative, integral and bounded GBL-algebras form a subvariety of residuated lattices which provides the algebraic semantics of an interesting common fragment of intuitionistic logic and of several fuzzy logics. It is known that both the equational theory and the quasiequational theory of commutative GBL-algebras are decidable (in contrast to the noncommutative case), but their complexity has...

A longstanding open problem is whether there exists a non-syntactical model of the untyped λ-calculus whose theory is exactly the least λ-theory λβ . In this paper we investigate the more general question of whether the equational/order theory of a model of the untyped λ-calculus can be recursively enumerable (r.e. for brevity). We introduce a notion of effective model of λ-calculus, which cove...

A longstanding open problem is whether there exists a non-syntactical model of the untyped λ-calculus whose theory is exactly the least λ-theory λβ . In this paper we investigate the more general question of whether the equational/order theory of a model of the untyped λ-calculus can be recursively enumerable (r.e. for brevity). We introduce a notion of effective model of λ-calculus, which cove...

A longstanding open problem is whether there exists a nonsyntactical model of the untyped λ-calculus whose theory is exactly the least λ-theory λβ. In this paper we investigate the more general question of whether the equational/order theory of a model of the untyped λ-calculus can be recursively enumerable (r.e. for brevity). We introduce a notion of effective model of λ-calculus, which covers...

The universal algebraic literature is rife with generalisations of discriminator varieties, whereby several investigators have tried to preserve in more general settings as much as possible of their structure theory. Here, we modify the definition of discriminator algebra by having the switching function project onto its third coordinate in case the ordered pair of its first two coordinates bel...

the aim of this paper is the study of fuzzy basis and dimensionof fuzzy hypervector spaces. in this regard, first the notions of fuzzy linearindependence and fuzzy basis are introduced and then some related results areobtained. in particular, it is shown that for a large class of fuzzy hypervectorspace the fuzzy basis exist. finally, dimension of a fuzzy hypervector space isdefined and the basi...