Displaying similar documents to “The distributivity numbers of finite products of P(ω)/fin”

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.

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

Modules commuting (via Hom) with some limits

Robert El Bashir, Tomáš Kepka (1998)

Fundamenta Mathematicae

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For every module M we have a natural monomorphism   Φ : ∐ i ∈ I H o m R ( A i , M ) → H o m R ( ∏ i ∈ I A i , M ) and we focus attention on the case when Φ is also an epimorphism. The corresponding modules M depend on thickness of the cardinal number card(I). Some other limits are also considered.

Examples for Souslin forcing

Haim Judah, Andrzej Rosłanowski, Saharon Shelah (1994)

Fundamenta Mathematicae

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We give several examples of Souslin forcing notions. For instance, we show that there exists a proper analytical forcing notion without ccc and with no perfect set of incompatible elements, we give an example of a Souslin ccc partial order without the Knaster property, and an example of a totally nonhomogeneous Souslin forcing notion.