Two conjectures regarding the stability of ω-categorical theories
A. Lachlan (1974)
Fundamenta Mathematicae
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A. Lachlan (1974)
Fundamenta Mathematicae
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John T. Baldwin, Kitty Holland (2001)
Fundamenta Mathematicae
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This is a sequel to [1]. Here we give careful attention to the difficulties of calculating Morley and U-rank of the infinite rank ω-stable theories constructed by variants of Hrushovski's methods. Sample result: For every k < ω, there is an ω-stable expansion of any algebraically closed field which has Morley rank ω × k. We include a corrected proof of the lemma in [1] establishing that the generic model is ω-saturated in the rank 2 case.
A. Lachlan (1972)
Fundamenta Mathematicae
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A. Lachlan (1980)
Fundamenta Mathematicae
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J. Wierzejewski (1977)
Fundamenta Mathematicae
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Frank O. Wagner (2003)
Fundamenta Mathematicae
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A small profinite m-stable group has an open abelian subgroup of finite ℳ-rank and finite exponent.
Robert J. Archbold, Eberhard Kaniuth (2006)
Studia Mathematica
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Let (G,X) be a transformation group, where X is a locally compact Hausdorff space and G is a compact group. We investigate the stable rank and the real rank of the transformation group C*-algebra C₀(X)⋊ G. Explicit formulae are given in the case where X and G are second countable and X is locally of finite G-orbit type. As a consequence, we calculate the ranks of the group C*-algebra C*(ℝⁿ ⋊ G), where G is a connected closed subgroup of SO(n) acting on ℝⁿ by rotation.
Gerald Sacks (1979)
Fundamenta Mathematicae
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Raymond Mortini (1992)
Studia Mathematica
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We present an example of a subalgebra with infinite stable rank in the algebra of all bounded analytic functions in the unit disk.
Anand Pillay (1980-1982)
Groupe d'étude de théories stables
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Joan Josep Carmona, Julià Cufí, Pere Menal (1992)
Publicacions Matemàtiques
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In this paper we prove a general result for the ring H(U) of the analytic functions on an open set U in the complex plane which implies that H(U) has not unit-1-stable rank and that has some other interesting consequences. We prove also that in H(U) there are no totally reducible elements different from the zero function.
Vincent Lee, Mark Nadel (1977)
Fundamenta Mathematicae
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Raymond Mortini (2014)
Annales Polonici Mathematici
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It is shown how to embed the polydisk algebras (finite and infinite ones) into the disk algebra A(𝔻̅). As a consequence, one obtains uniform closed subalgebras of A(𝔻̅) which have arbitrarily prescribed stable ranks.
Sy-David Friedman (2016)
Fundamenta Mathematicae
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In the author's 2012 paper, the V-definable Stable Core 𝕊 = (L[S],S) was introduced. It was shown that V is generic over 𝕊 (for 𝕊-definable dense classes), each V-definable club contains an 𝕊-definable club, and the same holds with 𝕊 replaced by (HOD,S), where HOD denotes Gödel's inner model of hereditarily ordinal-definable sets. In the present article we extend this to models of class theory by introducing the V-definable Enriched Stable Core 𝕊* = (L[S*],S*). As an application...
Predrag Tanović (2001)
Fundamenta Mathematicae
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We prove: Theorem. If T is a countable, complete, stable, first-order theory having an infinite set of constants with different interpretations, then I(T,ℵ₀) ≥ ℵ₀.
M. C. Laskowski, S. Shelah (2006)
Fundamenta Mathematicae
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We characterize the stable theories T for which the saturated models of T admit decompositions. In particular, we show that countable, shallow, stable theories with NDOP have this property.