The Borel cardinality of the quotient of the power set of the natural numbers by the ideal Z0 of asymptotically zero-density sets is shown to be the same as that of the equivalence relation induced by the classical Banach space c0. We also show that a large collection of ideals introduced by Louveau and Veličkovič, with pairwise incomparable Borel cardinality, are all Borel reducible to c0. Thi...

A T-fuzzy equivalence relation is a fuzzy binary relation on a set X which is reflexive, symmetric and T-transitive for a t-norm T. Recently, Mesiar et al. [R. Mesiar, B. Reusch, H. Thiele, Fuzzy equivalence relations and fuzzy partitions, J. Multi-Valued Logic Soft Comput. 12 (2006) 167–181] have generalised the t-norm T to any general conjunctor C and investigated the minimal assumptions requ...

We present an efficient equivalence-checking algorithm for a propositional model of programs with semantics based on (what we call) progressive monoids on the finite set of statements generated by relations of a specific form. We consider arbitrary set of relations for commutativity (relations of the form ab = ba for statements a, b) and left absorption (relations of the form ab = b for stateme...

Classical classification and clustering based on equivalence relations are very important tools in decision-making. An equivalence relation is usually determined by properties of objects in a given domain. When making decision, anything that can be spoken about in the subject position of a natural sentence is an object, properties of which are fundamental elements of the knowledge of the given ...

We will show how reaching consensus among n individuals communicating in pairs depends on the topology of the communications graph. In particular we show that the consensus on the value of union consistent function is guaranteed in any non-cyclic fair protocol. We also anylyze protocols where individuals exchange (simultaneously) information in pairs. Finally we prove a surprising result that a...

Recently, there has been a growing interest in understanding the complexity of common analytic equivalence relations between separable Banach spaces via the notion of Borel reducibility in descriptive set theory (see [Bos] [FG] [FLR] [FR1] [FR2] [Me]). In general, the notion of Borel reducibility yields a hierarchy (though not linear) among equivalence relations in terms of their relative compl...