Displaying similar documents to “On the diophantine equation f ( a m , y ) = b n ”

Linear orders and MA + ¬wKH

Zoran Spasojević (1995)

Fundamenta Mathematicae

Similarity:

I prove that the statement that “every linear order of size 2 ω can be embedded in ( ω ω , ≪ ) ” is consistent with MA + ¬ wKH.

Wildness in the product groups

G. Hjorth (2000)

Fundamenta Mathematicae

Similarity:

Non-abelian Polish groups arising as countable products of countable groups can be tame in arbitrarily complicated ways. This contrasts with some results of Solecki who revealed a very different picture in the abelian case.

Choice principles in Węglorz’ models

N. Brunner, Paul Howard, Jean Rubin (1997)

Fundamenta Mathematicae

Similarity:

Węglorz' models are models for set theory without the axiom of choice. Each one is determined by an atomic Boolean algebra. Here the algebraic properties of the Boolean algebra are compared to the set theoretic properties of the model.

Algebraic ramifications of the common extension problem for group-valued measures

Rüdiger Göbel, R. Shortt (1994)

Fundamenta Mathematicae

Similarity:

Let G be an Abelian group and let μ: A → G and ν: B → G be finitely additive measures (charges) defined on fields A and B of subsets of a set X. It is assumed that μ and ν agree on A ∩ B, i.e. they are consistent. The existence of common extensions of μ and ν is investigated, and conditions on A and B facilitating such extensions are given.

A Lefschetz-type coincidence theorem

Peter Saveliev (1999)

Fundamenta Mathematicae

Similarity:

A Lefschetz-type coincidence theorem for two maps f,g: X → Y from an arbitrary topological space to a manifold is given: I f g = λ f g , that is, the coincidence index is equal to the Lefschetz number. It follows that if λ f g ≠ 0 then there is an x ∈ X such that f(x) = g(x). In particular, the theorem contains well-known coincidence results for (i) X,Y manifolds, f boundary-preserving, and (ii) Y Euclidean, f with acyclic fibres. It also implies certain fixed point results for multivalued maps with “point-like”...