Families of Borel equivalence relations and quasiorders that are cofinal with respect to the Borel reducibility ordering, ≤B , are constructed. There is an analytic ideal on ù generating a complete analytic equivalence relation and any Borel equivalence relation reduces to one generated by a Borel ideal. Several Borel equivalence relations, among them Lipschitz isomorphism of compact metric spa...

The transitive closure of a reflexive, symmetric, analytic relation is an analytic equivalence relation. Does some smaller class contain the transitive closure of every reflexive, symmetric, closed relation? An essentially negative answer is provided here. Every analytic equivalence relation on an arbitrary Polish space is Borel embeddable in the transitive closure of the union of two smooth Bo...

Any map of schemes X → Y defines an equivalence relation R = X ×Y X → X × X, the relation of ”being in the same fiber”. We have shown elsewhere that not every equivalence relation has this form, even if it is assumed to be finite. By contrast, we prove here that every toric equivalence relation on an affine toric variety does come from a morphism and that quotients by finite toric equivalence r...

Let E,F be equivalence relations on N. We say that E is computably reducible to F , written E ≤ F , if there is a computable function p : N→ N such that xEy ↔ p(x)Fp(y). We show that several natural Σ 3 equivalence relations are in fact Σ 3 complete for this reducibility. Firstly, we show that one-one equivalence of computably enumerable sets, as an equivalence relation on indices, is Σ 3 compl...

This paper compares two models of concurrency, Milner's Calculus of Communicating Systems (CCS) and the failures model of Communicating Sequential Processes (CSP) developed by Hoare, Brookes and Roscoe. By adapting Milner's synchronisation trees to serve as notation for both CCS and CSP, we are able to define a representation mapping for CSP processes. We define an equivalence relation on synch...

The aim of this paper is the study of a covering of a max-mingeneral fuzzy automaton by another, admissible relations, admissiblepartitions of a max-min general fuzzy automaton,$tilde{delta}$-orthogonality of admissible partitions, irreduciblemax-min general fuzzy automata. Then we obtain the relationshipsbetween them.  

We consider the equivalence relation of isometry of separable, complete metric spaces, and show that any equivalence relation induced by a Borel action of a Polish group on a Polish space is Borel reducible to this isometry relation. We also consider the isometry relation restricted to various classes of metric spaces, and produce lower bounds for the complexity in terms of the Borel reducibili...

This paper demonstrates the importance of relation equivalence for entity translation pair discovery. Existing approach of understanding relation equivalence has focused on using explicit features of cooccurring entities. In this paper, we explore latent features of temporality for understanding relation equivalence, and empirically show that the explicit and latent features complement each oth...

The notion of data type speciication reenement is discussed in a setting of System F and the logic for parametric polymorphism of Plotkin and Abadi. At rst order, one gets a notion of speciication reenement up to observational equivalence in the logic simply by using Luo's formalism. This paper generalises this notion to abstract data types whose signatures contain higher-order and polymorphic ...