Upper bounds for least witnesses and generating sets
Ronald Joseph Burthe Jr. (1997)
Acta Arithmetica
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Ronald Joseph Burthe Jr. (1997)
Acta Arithmetica
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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., 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).
Yuri Bilu, Guillaume Hanrot (1999)
Acta Arithmetica
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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
Christian Ballot (1999)
Acta Arithmetica
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Karl K. Norton (1998)
Acta Arithmetica
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M. Stanley (1995)
Fundamenta Mathematicae
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