scholarly journals ON THE EXISTENCE OF LARGE ANTICHAINS FOR DEFINABLE QUASI-ORDERS

2019 ◽  
Vol 85 (1) ◽  
pp. 103-108
Author(s):  
BENJAMIN D. MILLER ◽  
ZOLTÁN VIDNYÁNSZKY
Keyword(s):  
Equivalence Relations ◽  
Perfect Set ◽  
Analogous Theorem

AbstractWe simultaneously generalize Silver’s perfect set theorem for co-analytic equivalence relations and Harrington-Marker-Shelah’s Dilworth-style perfect set theorem for Borel quasi-orders, establish the analogous theorem at the next definable cardinal, and give further generalizations under weaker definability conditions.

On non-wellfounded iterations of the perfect set forcing

1999 ◽  
Vol 64 (2) ◽  
pp. 551-574 ◽  
Author(s):  
Vladimir Kanovei
Keyword(s):  
Partially Ordered Set ◽  
Short Proof ◽  
Ordered Set ◽  
Equivalence Relations ◽  
Cardinal Invariant ◽  
Selection Principle ◽  
Partially Ordered ◽  
Transitive Model ◽  
Perfect Set

AbstractWe prove that if I is a partially ordered set in a countable transitive model of ZFC then can be extended by a generic sequence of reals ai, i ∈ I, such that is preserved and every ai is Sacks generic over [〈aj: j < i〉]. The structure of the degrees of -constructibility of reals in the extension is investigated.As applications of the methods involved, we define a cardinal invariant to distinguish product and iterated Sacks extensions, and give a short proof of a theorem (by Budinas) that in ω2-iterated Sacks extension of L the Burgess selection principle for analytic equivalence relations holds.

Thin equivalence relations and effective decompositions

1993 ◽  
Vol 58 (4) ◽  
pp. 1153-1164 ◽  
Author(s):  
Greg Hjorth
Keyword(s):  
Equivalence Relation ◽  
Equivalence Classes ◽  
Equivalence Relations ◽  
Perfect Set

AbstractLet E be a equivalence relation for which there does not exist a perfect set of inequivalent reals. If 0* exists or if V is a forcing extension of L, then there is a good well-ordering of the equivalence classes.

scholarly journals The Laczkovich-Komjáth property for coanalytic equivalence relations

2010 ◽  
Vol 75 (3) ◽  
pp. 1091-1101 ◽  
Author(s):  
Su Gao ◽  
Steve Jackson ◽  
Vincent Kieftenbeld
Keyword(s):  
Equivalence Relation ◽  
Polish Space ◽  
Equivalence Classes ◽  
Equivalence Relations ◽  
Perfect Set

AbstractLet E be a coanalytic equivalence relation on a Polish space X and (An)n∈ω a sequence of analytic subsets of X. We prove that if lim supn∈kAn meets uncountably many E-equivalence classes for every K ∈ [ω]ω, then there exists K ∈ [ω]ω such that ∩n∈kAn contains a perfect set of pairwise E-inequivalent elements.

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

A COMBINATORIAL CORE OF THE ITERATED PERFECT SET MODEL

1999 ◽  
Vol 25 (1) ◽  
pp. 137
Author(s):  
Ciesielski
Keyword(s):  
Perfect Set

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.

scholarly journals Nonlinear Conditions for Ultradifferentiability

2021 ◽  
Author(s):  
David Nicolas Nenning ◽  
Armin Rainer ◽  
Gerhard Schindl
Keyword(s):  
General Validity ◽  
Dimension One ◽  
Analogous Theorem

AbstractA remarkable theorem of Joris states that a function f is $$C^\infty $$ C ∞ if two relatively prime powers of f are $$C^\infty $$ C ∞ . Recently, Thilliez showed that an analogous theorem holds in Denjoy–Carleman classes of Roumieu type. We prove that a division property, equivalent to Joris’s result, is valid in a wide variety of ultradifferentiable classes. Generally speaking, it holds in all dimensions for non-quasianalytic classes. In the quasianalytic case we have general validity in dimension one, but we also get validity in all dimensions for certain quasianalytic classes.

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.

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