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Prediction problems and ultrafilters on ω

Alan D. Taylor (2012)

Fundamenta Mathematicae

We consider prediction problems in which each of a countably infinite set of agents tries to guess his own hat color based on the colors of the hats worn by the agents he can see, where who can see whom is specified by a graph V on ω. Our interest is in the case in which 𝓤 is an ultrafilter on the set of agents, and we seek conditions on 𝓤 and V ensuring the existence of a strategy such that the set of agents guessing correctly is of 𝓤-measure one. A natural necessary condition is the absence...

Rainbow Ramsey theorems for colorings establishing negative partition relations

András Hajnal (2008)

Fundamenta Mathematicae

Given a function f, a subset of its domain is a rainbow subset for f if f is one-to-one on it. We start with an old Erdős problem: Assume f is a coloring of the pairs of ω₁ with three colors such that every subset A of ω₁ of size ω₁ contains a pair of each color. Does there exist a rainbow triangle? We investigate rainbow problems and results of this style for colorings of pairs establishing negative "square bracket" relations.

Recent developments in the theory of partitions.

Di Prisco, Carlos Augusto (1999)

Boletín de la Asociación Matemática Venezolana

Rectangular square-bracket operation for successor of regular cardinals

Assaf Rinot, Stevo Todorcevic (2013)

Fundamenta Mathematicae

We give a uniform proof that $λ ⁺ ↛ [λ ⁺; λ ⁺] ²_{λ ⁺}$ holds for every regular cardinal λ.

Semiring of Sets

Roland Coghetto (2014)

Formalized Mathematics

Schmets [22] has developed a measure theory from a generalized notion of a semiring of sets. Goguadze [15] has introduced another generalized notion of semiring of sets and proved that all known properties that semiring have according to the old definitions are preserved. We show that this two notions are almost equivalent. We note that Patriota [20] has defined this quasi-semiring. We propose the formalization of some properties developed by the authors.

Semiring of Sets: Examples

Roland Coghetto (2014)

Formalized Mathematics

This article proposes the formalization of some examples of semiring of sets proposed by Goguadze [8] and Schmets [13].

Spaces related to gamma-sets

Filippo Cammaroto, Ljubiša Kočinac (2006)

Matematički Vesnik

$T$ -equivalences generated by shape function on the real line

Dug Hun Hong (2003)

Kybernetika

This paper is devoted to give a new method of generating T-equivalence using shape function and finding the exact calculation formulas of T-equivalence induced by shape function on the real line. Some illustrative examples are given.

The covering number for category and partition relations on $P_{ω} (λ)$

Pierre Matet (2002)

Fundamenta Mathematicae

We show that cov(M) is the least infinite cardinal λ such that $P_{ω} (λ)$ (the set of all finite subsets of λ ) fails to satisfy a certain natural generalization of Ramsey’s Theorem.

Unions of subquasigroups

Tomáš Kepka, Pavel Příhoda, Jan Šťovíček (2004)

Acta Universitatis Carolinae. Mathematica et Physica

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