On a problem of Eisenstein
Peter Stevenhagen (1996)
Acta Arithmetica
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Peter Stevenhagen (1996)
Acta Arithmetica
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Ilijas Farah (1996)
Fundamenta Mathematicae
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We investigate some natural questions about the class of posets which can be embedded into ⟨ω,≤*⟩. Our main tool is a simple ccc forcing notion which generically embeds a given poset E into ⟨ω,≤*⟩ and does this in a “minimal” way (see Theorems 9.1, 10.1, 6.1 and 9.2).
M. Losada, Stevo Todorčević (2000)
Fundamenta Mathematicae
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We give an affirmative answer to problem DJ from Fremlin’s list [8] which asks whether implies that every uncountable Boolean algebra has an uncountable set of pairwise incomparable elements.
Su Gao (2000)
Fundamenta Mathematicae
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We study the isomorphism relation of invariant Borel classes of countable mono-unary algebras and prove a strong dichotomy theorem.
J.-L. Colliot-Thélène, A. N. Skorobogatov, Sir Peter Swinnerton-Dyer (1997)
Acta Arithmetica
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Christopher McCord (1997)
Fundamenta Mathematicae
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Nielsen theory, originally developed as a homotopy-theoretic approach to fixed point theory, has been translated and extended to various other problems, such as the study of periodic points, coincidence points and roots. In this paper, the techniques of Nielsen theory are applied to the study of intersections of maps. A Nielsen-type number, the Nielsen intersection number NI(f,g), is introduced, and shown to have many of the properties analogous to those of the Nielsen fixed point number....
D. Benson, G. Gnacadja (1999)
Fundamenta Mathematicae
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Let k be a field and G a finite group. By analogy with the theory of phantom maps in topology, a map f : M → ℕ between kG-modules is said to be phantom if its restriction to every finitely generated submodule of M factors through a projective module. We investigate the relationships between the theory of phantom maps, the algebraic theory of purity, and Rickard's idempotent modules. In general, adding one to the pure global dimension of kG gives an upper bound for the number of phantoms...