Displaying similar documents to “On products of Radon measures”

Definability within structures related to Pascal’s triangle modulo an integer

Alexis Bès, Ivan Korec (1998)

Fundamenta Mathematicae

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Let Sq denote the set of squares, and let S Q n be the squaring function restricted to powers of n; let ⊥ denote the coprimeness relation. Let B n ( x , y ) = ( x + y x ) M O D n . For every integer n ≥ 2 addition and multiplication are definable in the structures ⟨ℕ; Bn,⊥⟩ and ⟨ℕ; Bn,Sq⟩; thus their elementary theories are undecidable. On the other hand, for every prime p the elementary theory of ⟨ℕ; Bp,SQp⟩ is decidable.

Hausdorff ’s theorem for posets that satisfy the finite antichain property

Uri Abraham, Robert Bonnet (1999)

Fundamenta Mathematicae

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Hausdorff characterized the class of scattered linear orderings as the least family of linear orderings that includes the ordinals and is closed under ordinal summations and inversions. We formulate and prove a corresponding characterization of the class of scattered partial orderings that satisfy the finite antichain condition (FAC).  Consider the least class of partial orderings containing the class of well-founded orderings that satisfy the FAC and is closed under the following operations:...

Ordinary differential equations and descriptive set theory: uniqueness and globality of solutions of Cauchy problems in one dimension

Alessandro Andretta, Alberto Marcone (1997)

Fundamenta Mathematicae

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We study some natural sets arising in the theory of ordinary differential equations in one variable from the point of view of descriptive set theory and in particular classify them within the Borel hierarchy. We prove that the set of Cauchy problems for ordinary differential equations which have a unique solution is ∏ 2 0 -complete and that the set of Cauchy problems which locally have a unique solution is ∑ 3 0 -complete. We prove that the set of Cauchy problems which have a global solution is...

Classical-type characterizations of non-metrizable ANE(n)-spaces

Valentin Gutev, Vesko Valov (1994)

Fundamenta Mathematicae

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The Kuratowski-Dugundji theorem that a metrizable space is an absolute (neighborhood) extensor in dimension n iff it is L C n - 1 C n - 1 (resp., L C n - 1 ) is extended to a class of non-metrizable absolute (neighborhood) extensors in dimension n. On this base, several facts concerning metrizable extensors are established for non-metrizable ones.

Topological realization of a family of pseudoreflection groups

Dietrich Notbohm (1998)

Fundamenta Mathematicae

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We are interested in a topological realization of a family of pseudoreflection groups G ⊂ G L ( n , F p ) ; i.e. we are looking for topological spaces whose mod-p cohomology is isomorphic to the ring of invariants F p [ x 1 , . . . , x n ] G . Spaces of this type give partial answers to a problem of Steenrod, namely which polynomial algebras over F p can appear as the mod-p cohomology of a space. The family under consideration is given by pseudoreflection groups which are subgroups of the wreath product ℤ / q ≀ Σ n where q divides p - 1 and...

Accessibility of typical points for invariant measures of positive Lyapunov exponents for iterations of holomorphic maps

Feliks Przytycki (1994)

Fundamenta Mathematicae

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We prove that if A is the basin of immediate attraction to a periodic attracting or parabolic point for a rational map f on the Riemann sphere, if A is completely invariant (i.e. f - 1 ( A ) = A ), and if μ is an arbitrary f-invariant measure with positive Lyapunov exponents on ∂A, then μ-almost every point q ∈ ∂A is accessible along a curve from A. In fact, we prove the accessibility of every “good” q, i.e. one for which “small neigh bourhoods arrive at large scale” under iteration of f. This generalizes...

Cofinal Σ 1 1 and Π 1 1 subsets of ω ω

Gabriel Debs, Jean Saint Raymond (1999)

Fundamenta Mathematicae

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We study properties of ∑ 1 1 and π 1 1 subsets of ω ω that are cofinal relative to the orders ≤ (≤*) of full (eventual) domination. We apply these results to prove that the topological statement “Any compact covering mapping from a Borel space onto a Polish space is inductively perfect” is equivalent to the statement " ∀ α ∈ ω ω , ω ω ∩ L ( α ) is bounded for ≤*".

Endomorphism algebras over large domains

Rüdiger Göbel, Simone Pabst (1998)

Fundamenta Mathematicae

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The paper deals with realizations of R-algebras A as endomorphism algebras End G ≅ A of suitable R-modules G over a commutative ring R. We are mainly interested in the case of R having "many prime ideals", such as R = ℝ[x], the ring of real polynomials, or R a non-discrete valuation domain

The distributivity numbers of finite products of P(ω)/fin

Saharon Shelah, Otmar Spinas (1998)

Fundamenta Mathematicae

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Generalizing [ShSp], for every n < ω we construct a ZFC-model where ℌ(n), the distributivity number of r.o. ( P ( ω ) / f i n ) n , is greater than ℌ(n+1). This answers an old problem of Balcar, Pelant and Simon (see [BaPeSi]). We also show that both Laver and Miller forcings collapse the continuum to ℌ(n) for every n < ω, hence by the first result, consistently they collapse it below ℌ(n).