Elections generate all binary relations on infinite sets

2016 ◽  
Vol 84 ◽  
pp. 105-108 ◽  
Author(s):  
Vicki Knoblauch
Keyword(s):  
Binary Relations ◽  
Infinite Sets

scholarly journals Finitely Supported Binary Relations between Infinite Atomic Sets

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2028
Author(s):  
Andrei Alexandru ◽  
Gabriel Ciobanu
Keyword(s):  
Higher Order ◽  
Infinite Subset ◽  
Closure Property ◽  
Binary Relations ◽  
Finite Support ◽  
Finite Sets ◽  
Infinite Sets ◽  
Support Principle ◽  
Countably Infinite ◽  
Finiteness Properties

In the framework of finitely supported atomic sets, by using the notion of atomic cardinality and the T-finite support principle (a closure property for supports in some higher-order constructions), we present some finiteness properties of the finitely supported binary relations between infinite atomic sets. Of particular interest are finitely supported Dedekind-finite sets because they do not contain finitely supported, countably infinite subsets. We prove that the infinite sets ℘fs(Ak×Al), ℘fs(Ak×℘m(A)), ℘fs(℘n(A)×Ak) and ℘fs(℘n(A)×℘m(A)) do not contain uniformly supported infinite subsets. Moreover, the functions space ZAm does not contain a uniformly supported infinite subset whenever Z does not contain a uniformly supported infinite subset. All these sets are Dedekind-finite in the framework of finitely supported structures.

Computable numberings of families of infinite sets

2019 ◽  
Vol 58 (3) ◽  
pp. 334-343
Author(s):  
M. V. Dorzhieva
Keyword(s):  
Computable Numberings ◽  
Infinite Sets

FACTOR ANALYSIS OF GEOGRAPHIC COORDINATES AT POINTS OF THE CHANNEL OF A SMALL RIVER ON SPACE IMAGES

2020 ◽  
Author(s):  
Peter Matveevich Mazurkin ◽  
Yana Oltgovna Georgieva
Keyword(s):  
Correlation Coefficient ◽  
Geographical Location ◽  
Small River ◽  
Binary Relations ◽  
Catchment Basin ◽  
Space Images ◽  
The North ◽  
Inverse Effect ◽  
Characteristic Points ◽  
Fractal Representation

The purpose of the article is the analysis of asymmetric wavelets in binary relations between three coordinates at 290 characteristic points from the source to the mouth of the small river Irovka. The hypsometric characteristic is the most important property of the relief. The Irovka River belongs to a low level, at the mouth it is 89 m high, and at the source it is 148 m above sea level. Modeling of binary relations with latitude, longitude, and height has shown that local latitude receives the greatest quantum certainty. In this case, all paired regularities received a correlation coefficient of more than 0.95. Such a high adequacy of wave patterns shows that geomorphology can go over to the wave multiple fractal representation of the relief. The Irovka River is characterized by a small anthropogenic impact, therefore, the relief over a length of 69 km has the natural character of the oscillatory adaptation of a small river to the surface of the Vyatka Uval from its eastern side. This allows us to proceed to the analysis of the four tributaries of the small river Irovka, as well as to model the relief of the entire catchment basin of 917 km2. The greatest adequacy with a correlation coefficient of 0.9976 was obtained by the influence of latitude on longitude, that is, the geographical location of the relief of the river channel with respect to the geomorphology of the Vyatka Uval. In second place with a correlation of 0.9967 was the influence of the height of the points of the channel of the small river on local longitude and it is also mainly determined by the relief of the Vyatka Uval. In third place was the effect of latitude on height with a correlation coefficient of 0.9859. And in last sixth place is the inverse effect of altitude on local latitude in the North-South direction.

On algebras of binary relations with conjunctive operations

2021 ◽  
Vol 82 (3) ◽  
Author(s):  
Dmitry A. Bredikhin
Keyword(s):  
Binary Relations

scholarly journals Finite representability of semigroups with demonic refinement

2021 ◽  
Vol 82 (2) ◽  
Author(s):  
Robin Hirsch ◽  
Jaš Šemrl
Keyword(s):  
Partial Order ◽  
Turing Machines ◽  
Binary Relations ◽  
Finite Representation ◽  
First Order ◽  
Finite Structures ◽  
Finite Base ◽  
Finite Set ◽  
Finite Representability ◽  
Representation Class

AbstractThe motivation for using demonic calculus for binary relations stems from the behaviour of demonic turing machines, when modelled relationally. Relational composition (; ) models sequential runs of two programs and demonic refinement ($$\sqsubseteq $$ ⊑ ) arises from the partial order given by modeling demonic choice ($$\sqcup $$ ⊔ ) of programs (see below for the formal relational definitions). We prove that the class $$R(\sqsubseteq , ;)$$ R ( ⊑ , ; ) of abstract $$(\le , \circ )$$ ( ≤ , ∘ ) structures isomorphic to a set of binary relations ordered by demonic refinement with composition cannot be axiomatised by any finite set of first-order $$(\le , \circ )$$ ( ≤ , ∘ ) formulas. We provide a fairly simple, infinite, recursive axiomatisation that defines $$R(\sqsubseteq , ;)$$ R ( ⊑ , ; ) . We prove that a finite representable $$(\le , \circ )$$ ( ≤ , ∘ ) structure has a representation over a finite base. This appears to be the first example of a signature for binary relations with composition where the representation class is non-finitely axiomatisable, but where the finite representation property holds for finite structures.

Program structure definition using binary relations

1976 ◽  
Vol 11 (12) ◽  
pp. 38-55
Author(s):  
Lars Kahn
Keyword(s):  
Binary Relations ◽  
Program Structure

RELEVANCE LOGIC AND THE CALCULUS OF RELATIONS

2010 ◽  
Vol 3 (1) ◽  
pp. 41-70 ◽  
Author(s):  
ROGER D. MADDUX
Keyword(s):  
Propositional Logic ◽  
Relevance Logic ◽  
Binary Relations ◽  
Classical Propositional Logic

Sound and complete semantics for classical propositional logic can be obtained by interpreting sentences as sets. Replacing sets with commuting dense binary relations produces an interpretation that turns out to be sound but not complete for R. Adding transitivity yields sound and complete semantics for RM, because all normal Sugihara matrices are representable as algebras of binary relations.

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