The states of a computing system bear information and change time, while its events bear time and change information. We develop a primitive algebraic model of this duality of time and information for rigid local computation, or straightline code, in the absence of choice and concurrency, where time and information are linearly ordered. This shows the duality of computation to be more fundament...

What are variables, and what is universal quantification over a variable? Nominal sets are a notion of ‘sets with names’, and using equational axioms in nominal algebra these names can be given substitution and quantification actions. So we can axiomatise first-order logic as a nominal logical theory. We can then seek a nominal sets representation theorem in which predicates are interpreted as ...

This paper studies finitary modal logics as specification languages for Set-coalgebras (coalgebras on the category of sets) using Stone duality. It is wellknown that Set-coalgebras are not semantically adequate for finitary modal logics in the sense that bisimilarity does not in general coincide with logical equivalence. Stone-coalgebras (coalgebras over the category of Stone spaces), on the ot...

We exhibit Pontryagin duality as a special case of Stone in continuous logic setting. More specifically, given an abelian topological group A, and F the family (group) homomorphisms from A to circle T, then, viewing (A,+) equipped with collection structure M, we show that local type space SF(M) is precisely dual where latter considered discrete group. conclude, using (between compact groups), B...

We develop a uniform coalgebraic approach to J\'onsson-Tarski and Thomason type dualities for various classes of neighborhood frames algebras. In the first part paper we construct an endofunctor on category complete atomic Boolean algebras that is dual double powerset functor $\mathsf{Set}$. This allows us show duality can be viewed as algebra-coalgebra duality. generalize this any class presen...

This paper is a continuation of [8] and in it some applications of the methods and results of [8] and of [28, 7, 24, 9, 10, 11] are given. In particular, some generalizations of the Stone Duality Theorem [28] are obtained; a completion theorem for local contact Boolean algebras is proved; a direct proof of the Ponomarev’s solution [22] of Birkhoff’s Problem 72 [5] is found, and the spaces which...

A stepping stone model with site space a continuous, hierarchical group is constructed via duality with a system of (delayed) coalescing \stable" L evy processes. This model can be understood as a continuum limit of discrete state-space, two allele, genetics models with hierarchically structured resampling and migration. The existence of a process rescaling limit on suitable large space and tim...

In this note we introduce and study algebras ( L , V, A, 1, 0,l) of type (2,2,1,1,1) such that ( L , V, A, 0 , l ) is a bounded distributive lattice and -,is an operator that satisfies the conditions -,(a V b ) = -,a A -,b and -0 = 1. We develop the topological duality between these algebras and Priestley spaces with a relation. In addition, we characterize the congruences and the subalgebras o...