On Davenport's bound for the degree of f³ - g² and Riemann's Existence Theorem
Umberto Zannier (1995)
Acta Arithmetica
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Umberto Zannier (1995)
Acta Arithmetica
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James Cummings, Mirna Džamonja, Saharon Shelah (1995)
Fundamenta Mathematicae
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Carlos González (1995)
Fundamenta Mathematicae
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We investigate the relative consistency and independence of statements which imply the existence of various kinds of dense orders, including dense linear orders. We study as well the relationship between these statements and others involving partition properties. Since we work in ZF (i.e. without the Axiom of Choice), we also analyze the role that some weaker forms of AC play in this context
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).
Joan Hart, Kenneth Kunen (1999)
Fundamenta Mathematicae
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We prove the following theorem: Given a⊆ω and , if for some and all u ∈ WO of length η, a is , then a is .We use this result to give a new, forcing-free, proof of Leo Harrington’s theorem: -Turing-determinacy implies the existence of .
Ludomir Newelski (1996)
Fundamenta Mathematicae
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Assume p* is a meager type in a superstable theory T. We investigate definability properties of p*-closure. We prove that if T has countable models then the multiplicity rank ℳ of every type p is finite. We improve Saffe’s conjecture.
Chris Miller, Patrick Speissegger (1999)
Fundamenta Mathematicae
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The open core of a structure ℜ := (ℝ,<,...) is defined to be the reduct (in the sense of definability) of ℜ generated by all of its definable open sets. If the open core of ℜ is o-minimal, then the topological closure of any definable set has finitely many connected components. We show that if every definable subset of ℝ is finite or uncountable, or if ℜ defines addition and multiplication and every definable open subset of ℝ has finitely many connected components, then the open core...