All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 3 Next

Displaying 41 – 60 of 123

Showing per page

Discrete n-tuples in Hausdorff spaces

Timothy J. Carlson, Neil Hindman, Dona Strauss (2005)

Fundamenta Mathematicae

We investigate the following three questions: Let n ∈ ℕ. For which Hausdorff spaces X is it true that whenever Γ is an arbitrary (respectively finite-to-one, respectively injective) function from ℕⁿ to X, there must exist an infinite subset M of ℕ such that Γ[Mⁿ] is discrete? Of course, if n = 1 the answer to all three questions is "all of them". For n ≥ 2 the answers to the second and third questions are the same; in the case n = 2 that answer is "those for which there are only finitely many points...

Dynamical characterization of C-sets and its application

Jian Li (2012)

Fundamenta Mathematicae

We set up a general correspondence between algebraic properties of βℕ and sets defined by dynamical properties. In particular, we obtain a dynamical characterization of C-sets, i.e., sets satisfying the strong Central Sets Theorem. As an application, we show that Rado systems are solvable in C-sets.

Dynamical properties of the automorphism groups of the random poset and random distributive lattice

Alexander S. Kechris, Miodrag Sokić (2012)

Fundamenta Mathematicae

A method is developed for proving non-amenability of certain automorphism groups of countable structures and is used to show that the automorphism groups of the random poset and random distributive lattice are not amenable. The universal minimal flow of the automorphism group of the random distributive lattice is computed as a canonical space of linear orderings but it is also shown that the class of finite distributive lattices does not admit hereditary order expansions with the Amalgamation Property....

Extended Ramsey theory for words representing rationals

Vassiliki Farmaki, Andreas Koutsogiannis (2013)

Fundamenta Mathematicae

Ramsey theory for words over a finite alphabet was unified in the work of Carlson, who also presented a method to extend the theory to words over an infinite alphabet, but subject to a fixed dominating principle. In the present work we establish an extension of Carlson's approach to countable ordinals and Schreier-type families developing an extended Ramsey theory for dominated words over a doubly infinite alphabet (in fact for ω-ℤ*-located words), and we apply this theory, exploiting the Budak-Işik-Pym...

Higher order spreading models

S. A. Argyros, V. Kanellopoulos, K. Tyros (2013)

Fundamenta Mathematicae

We introduce higher order spreading models associated to a Banach space X. Their definition is based on ℱ-sequences ( x s ) s ∈ ℱ with ℱ a regular thin family and on plegma families. We show that the higher order spreading models of a Banach space X form an increasing transfinite hierarchy ( ℳ ξ ( X ) ) ξ < ω ₁ . Each ℳ ξ ( X ) contains all spreading models generated by ℱ-sequences ( x s ) s ∈ ℱ with order of ℱ equal to ξ. We also study the fundamental properties of this hierarchy.

Ideal version of Ramsey's theorem

Rafał Filipów, Nikodem Mrożek, Ireneusz Recław, Piotr Szuca (2011)

Czechoslovak Mathematical Journal

We consider various forms of Ramsey's theorem, the monotone subsequence theorem and the Bolzano-Weierstrass theorem which are connected with ideals of subsets of natural numbers. We characterize ideals with properties considered. We show that, in a sense, Ramsey's theorem, the monotone subsequence theorem and the Bolzano-Weierstrass theorem characterize the same class of ideals. We use our results to show some versions of density Ramsey's theorem (these are similar to generalizations shown in [P....

Indestructible colourings and rainbow Ramsey theorems

Lajos Soukup (2009)

Fundamenta Mathematicae

We show that if a colouring c establishes ω₂ ↛ [(ω₁:ω)]² then c establishes this negative partition relation in each Cohen-generic extension of the ground model, i.e. this property of c is Cohen-indestructible. This result yields a negative answer to a question of Erdős and Hajnal: it is consistent that GCH holds and there is a colouring c:[ω₂]² → 2 establishing ω₂ ↛ [(ω₁:ω)]₂ such that some colouring g:[ω₁]² → 2 does not embed into c. It is also consistent that 2 ω ₁ is arbitrarily large, and there...

k -Ramsey classes and dimensions of graphs

Jan Kratochvíl (1995)

Commentationes Mathematicae Universitatis Carolinae

In this note, we introduce the notion of k -Ramsey classes of graphs and we reveal connections to intersection dimensions of graphs.

Currently displaying 41 – 60 of 123