Silvers’s perfect set theorem says that every Π1 equivalence relation over a polish space either has countably many equivalence classes or has a perfect set of inequivalent elements. We prove an analog where the equivalence relation is replaced by a Π1 dependence relation, and the perfect set of inequivalent elements is replaced by a perfect independent set. The dependence relation should satis...

We prove that orbit equivalence of measure preserving ergodic a.e. free actions of a countable group with the relative property (T) is a complete analytic equivalence relation.

A Borel equivalence relation on a Polish space is countable if all of its equivalence classes are countable. Standard examples of countable Borel equivalence relations (on the space of subsets of the integers) that occur in recursion theory are: recursive isomorphism, Turing equivalence, arithmetic equivalence, etc. There is a canonical hierarchy of complexity of countable Borel equivalence rel...

In this paper we introduce the smallest equivalence relation ξ∗ on a finite fuzzy hypergroup S such that the quotient group S/ξ∗, the set of all equivalence classes, is a solvable group. The characterization of solvable groups via strongly regular relation is investigated and several results on the topic are presented.

Kock, A. and I. Moerdijk, Every &endue comes from a local equivalence relation, Journal of Pure and Applied Algebra 82 (1992) 155-174. We first prove that, under suitable connectedness assumptions, the equivariant sheaves for a local equivalence relation on a space (or a locale) form an &endue topos. Our main result is that conversely, every &endue can be obtained in this way.

Gauge invariance is used to establish an equivalence relation between solutions of the time-independent and time-dependent Ginzburg-Landau equations that describe the same physical state of a superconductor. The equivalence relation shows how equilibrium conngurations are obtained as large-time asymptotic limits of solutions of the time-dependent Ginzburg-Landau equations.

The Rogers semilattice of effective programming systems (epses) is the collection of all effective numberings of the partial computable functions ordered such that θ ≤ ψ whenever θ-programs can be algorithmically translated into ψ-programs. Herein, it is shown that an eps ψ is minimal in this ordering if and only if, for each translation function t into ψ, there exists a computably enumerable e...

Roughly, we define a redundant relation in a database instance (dbi) as a k-ary relation R such that there is a first-order query which evaluated in the reduced dbi, gives us R. So, we can eliminate that relation R as long as the equivalence classes of the relation of equality of the first-order types for all k-tuples in the dbi are not altered. It turns out that in a fixed dbi, the problem of ...

The main tools in the theory of n-ary hyperstructures are the fundamental relations. The fundamental relation on an n-ary hypersemigroup is defined as the smallest equivalence relation so that the quotient would be the n-ary semigroup. In this paper we study neutral elements in n-ary hypersemigroups and introduce a new strongly compatible equivalence relation on an n-ary hypersemigroup so that ...

Bounded orbit injection equivalence is an equivalence relation defined on minimal free Cantor systems which is a candidate to generalize flip Kakutani equivalence to actions of the Abelian free groups on more than one generator. This paper characterizes bounded orbit injection equivalence in terms of a mild strengthening of Rieffel-Morita equivalence of the associated C*-crossed-product algebra...