Sets of natural numbers of positive density and cylindric set algebras of dimension 2

1981 ◽  
Vol 12 (1) ◽  
pp. 81-92 ◽  
Author(s):  
Paul Erdös ◽  
Vance Faber ◽  
Jean Larson
Keyword(s):  
Positive Density ◽  
Natural Numbers ◽  
Dimension 2 ◽  
Cylindric Set Algebras

Decidability of cylindric set algebras of dimension two and first-order logic with two variables

1999 ◽  
Vol 64 (4) ◽  
pp. 1563-1572 ◽  
Author(s):  
Maarten Marx ◽  
Szabolcs Mikulás
Keyword(s):  
Order Logic ◽  
First Order Logic ◽  
Universal Theory ◽  
Finite Model ◽  
Finite Model Property ◽  
First Order ◽  
Combinatorial Theorem ◽  
Finite Base ◽  
Dimension 2 ◽  
Cylindric Set Algebras

AbstractThe aim of this paper is to give a new proof for the decidability and finite model property of first-order logic with two variables (without function symbols), using a combinatorial theorem due to Herwig. The results are proved in the framework of polyadic equality set algebras of dimension two (Pse2). The new proof also shows the known results that the universal theory of Pse2 is decidable and that every finite Pse2 can be represented on a finite base. Since the class Cs2 of cylindric set algebras of dimension 2 forms a reduct of Pse2, these results extend to Cs2 as well.

Sur un critère de récurrence en dimension 2 pour les marches stationnaires, applications

1999 ◽  
Vol 19 (5) ◽  
pp. 1233-1245 ◽  
Author(s):  
J.-P. CONZE
Keyword(s):  
Dynamical System ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Lorentz Gas ◽  
Positive Density ◽  
Martingale Difference ◽  
Regular Functions ◽  
The Central Limit Theorem ◽  
Dimension 2

Let $(E,{\cal A},\mu,T)$ be a dynamical system and let $\Phi$ be a function defined on $E$ with values in $\mathbb{R}^2$. We give a criterion, the central limit theorem along subsequences of positive density, for the recurrence of the corresponding ‘stationary walk’ defined as the cocycle $\big(\sum^{n-1}_{j=0}\Phi(T^jx)\big)_{n\geq1}$.This criterion is satisfied by functions which are homologous to a martingale difference (a property which holds for regular functions in many systems). It can also be applied to the periodic Lorentz gas in the plane and shows recurrence for this model.

The Argument from (Natural) Numbers

2018 ◽  
Author(s):  
Tyron Goldschmidt
Keyword(s):  
Natural Numbers ◽  
Existence Of God ◽  
Divine Attribute ◽  
Rule Out

This chapter considers Plantinga’s argument from numbers for the existence of God. Plantinga sees divine psychologism as having advantages over both human psychologism and Platonism. The chapter begins with Plantinga’s description of the argument, including the relation of numbers to any divine attribute. It then argues that human psychologism can be ruled out completely. However, what rules it out might rule out divine psychologism too. It also argues that the main problem with Platonism might also be a problem with divine psychologism. However, it will, at the least, be less of a problem. In any case, there are alternative, possibly viable views about the nature of numbers that have not been touched by Plantinga’s argument. In addition, the chapter touches on the argument from properties, and its relation to the argument from numbers.

The Natural Numbers

2018 ◽  
Author(s):  
Øystein Linnebo
Keyword(s):  
Natural Number ◽  
Peano Arithmetic ◽  
Number Sequence ◽  
Natural Numbers ◽  
Ordinal Numbers ◽  
Cardinal Numbers

How are the natural numbers individuated? That is, what is our most basic way of singling out a natural number for reference in language or in thought? According to Frege and many of his followers, the natural numbers are cardinal numbers, individuated by the cardinalities of the collections that they number. Another answer regards the natural numbers as ordinal numbers, individuated by their positions in the natural number sequence. Some reasons to favor the second answer are presented. This answer is therefore developed in more detail, involving a form of abstraction on numerals. Based on this answer, a justification for the axioms of Dedekind–Peano arithmetic is developed.

Asymptotics with remainder term for moments of the total cycle number of random A-permutation

2021 ◽  
Vol 31 (1) ◽  
pp. 51-60
Author(s):  
Arsen L. Yakymiv
Keyword(s):  
Remainder Term ◽  
Random Permutation ◽  
Natural Numbers ◽  
Cycle Number ◽  
Fixed Set ◽  
Cycle Lengths

Abstract Dedicated to the memory of Alexander Ivanovich Pavlov. We consider the set of n-permutations with cycle lengths belonging to some fixed set A of natural numbers (so-called A-permutations). Let random permutation τ n be uniformly distributed on this set. For some class of sets A we find the asymptotics with remainder term for moments of total cycle number of τ n .

Ideal convergent sequence spaces of fuzzy star–shaped numbers

2021 ◽  
pp. 1-8
Author(s):  
Vakeel A. Khan ◽  
Umme Tuba ◽  
SK. Ashadul Rahama ◽  
Ayaz Ahmad
Keyword(s):  
Fuzzy Sets ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Natural Numbers

In 1990, Diamond [16] primarily established the base of fuzzy star–shaped sets, an extension of fuzzy sets and numerous of its properties. In this paper, we aim to generalize the convergence induced by an ideal defined on natural numbers ℕ , introduce new sequence spaces of fuzzy star–shaped numbers in ℝ n and examine various algebraic and topological properties of the new corresponding spaces as well. In support of our results, we provide several examples of these new resulting sequences.

scholarly journals k-Zumkeller labeling of super subdivision of some graphs

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
M. Basher
Keyword(s):  
Simple Graph ◽  
Natural Numbers ◽  
Injective Function ◽  
Planar Grid ◽  
Circular Ladder

AbstractA simple graph $$G=(V,E)$$ G = ( V , E ) is said to be k-Zumkeller graph if there is an injective function f from the vertices of G to the natural numbers N such that when each edge $$xy\in E$$ x y ∈ E is assigned the label f(x)f(y), the resulting edge labels are k distinct Zumkeller numbers. In this paper, we show that the super subdivision of path, cycle, comb, ladder, crown, circular ladder, planar grid and prism are k-Zumkeller graphs.

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