A theorem on ROD-hypersmooth equivalence relations in the Solovay model

2003 ◽  
Vol 49 (3) ◽  
pp. 299-304 ◽  
Author(s):  
Vladimir Kanovei ◽  
Michael Reeken
Keyword(s):  
Equivalence Relations ◽  
Solovay Model

scholarly journals An Ulm-type classification theorem for equivalence relations in Solovay model

1997 ◽  
Vol 62 (4) ◽  
pp. 1333-1351 ◽  
Author(s):  
Vladimir Kanovei
Keyword(s):  
Equivalence Relation ◽  
Binary Sequences ◽  
Classification Theorem ◽  
Equivalence Relations ◽  
Equality Relation ◽  
Solovay Model ◽  
Type Classification

AbstractWe prove that in the Solovay model, every OD equivalence relation, Ε, over the reals, either admits an OD reduction to the equality relation on the set of all countable (of length < ω1) binary sequences, or continuously embeds Ε0, the Vitali equivalence.If Ε is a (resp. ) relation then the reduction above can be chosen in the class of all Δ1 (resp. Δ2) functions.The proofs are based on a topology generated by OD sets.

Weakly precomplete equivalence relations in the Ershov hierarchy

2019 ◽  
Vol 58 (3) ◽  
pp. 297-319
Author(s):  
N. A. Bazhenov ◽  
B. S. Kalmurzaev
Keyword(s):  
Equivalence Relations ◽  
Ershov Hierarchy

Equivalence relations among inequalities for some relative operator entropies

Positivity ◽  
2020 ◽  
Vol 24 (5) ◽  
pp. 1503-1518
Author(s):  
Ismail Nikoufar ◽  
Maryam Fazlolahi
Keyword(s):  
Equivalence Relations

Fundamental relations and identities of fuzzy hyperalgebras

2021 ◽  
pp. 1-10
Author(s):  
Narjes Firouzkouhi ◽  
Abbas Amini ◽  
Chun Cheng ◽  
Mehdi Soleymani ◽  
Bijan Davvaz
Keyword(s):  
Universal Algebra ◽  
Equivalence Relation ◽  
Polynomial Function ◽  
Equivalence Relations ◽  
Fundamental Relation ◽  
Term Function ◽  
Biological Phenomena ◽  
Definition Of

Inspired by fuzzy hyperalgebras and fuzzy polynomial function (term function), some homomorphism properties of fundamental relation on fuzzy hyperalgebras are conveyed. The obtained relations of fuzzy hyperalgebra are utilized for certain applications, i.e., biological phenomena and genetics along with some elucidatory examples presenting various aspects of fuzzy hyperalgebras. Then, by considering the definition of identities (weak and strong) as a class of fuzzy polynomial function, the smallest equivalence relation (fundamental relation) is obtained which is an important tool for fuzzy hyperalgebraic systems. Through the characterization of these equivalence relations of a fuzzy hyperalgebra, we assign the smallest equivalence relation α i 1 i 2 ∗ on a fuzzy hyperalgebra via identities where the factor hyperalgebra is a universal algebra. We extend and improve the identities on fuzzy hyperalgebras and characterize the smallest equivalence relation α J ∗ on the set of strong identities.

Query Optimization in the Databases Distributed by Means of Product Equivalence Relations

1988 ◽  
Vol 11 (3) ◽  
pp. 241-265
Author(s):  
W. Marek ◽  
C. Rauszer
Keyword(s):  
Query Optimization ◽  
Selection Process ◽  
Distributed Databases ◽  
Optimization Techniques ◽  
Equivalence Relations ◽  
Database Operations ◽  
By Products

In this paper, we address the problem of query optimization in distributed databases. We show that horizontal partitions of databases, generated by products of equivalence relations, induce optimization techniques for the basic database operations (i.e., the selection, projection, and join operators). In the case of selection, our method allows for restriction of the number of blocks to be searched in the selection process and subsequent simplification of the selection formula at each block. For the natural join operation, we propose an algorithm that reduces the computation of fragments. Proofs of the correctness of our algorithms are also included.

scholarly journals L2-BETTI NUMBERS OF DISCRETE MEASURED GROUPOIDS

2005 ◽  
Vol 15 (05n06) ◽  
pp. 1169-1188 ◽  
Author(s):  
ROMAN SAUER
Keyword(s):  
Probability Space ◽  
Betti Numbers ◽  
Free Action ◽  
Countable Group ◽  
Equivalence Relations ◽  
Dimension Theory ◽  
Discrete Groups ◽  
Type Ii ◽  
Orbit Equivalent ◽  
Definition Of

There are notions of L2-Betti numbers for discrete groups (Cheeger–Gromov, Lück), for type II1-factors (recent work of Connes-Shlyakhtenko) and for countable standard equivalence relations (Gaboriau). Whereas the first two are algebraically defined using Lück's dimension theory, Gaboriau's definition of the latter is inspired by the work of Cheeger and Gromov. In this work we give a definition of L2-Betti numbers of discrete measured groupoids that is based on Lück's dimension theory, thereby encompassing the cases of groups, equivalence relations and holonomy groupoids with an invariant measure for a complete transversal. We show that with our definition, like with Gaboriau's, the L2-Betti numbers [Formula: see text] of a countable group G coincide with the L2-Betti numbers [Formula: see text] of the orbit equivalence relation [Formula: see text] of a free action of G on a probability space. This yields a new proof of the fact the L2-Betti numbers of groups with orbit equivalent actions coincide.

Establishing Equivalence Relations Using a Respondent-Type Training Procedure

1996 ◽  
Vol 46 (4) ◽  
pp. 685-706 ◽  
Author(s):  
Geraldine Leader ◽  
Dermot Barnes ◽  
Paul M. Smeets
Keyword(s):  
Equivalence Relations ◽  
Training Procedure
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