Canonical heights on the Jacobians of curves of genus 2 and the infinite descent
E. V. Flynn, N. P. Smart (1997)
Acta Arithmetica
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E. V. Flynn, N. P. Smart (1997)
Acta Arithmetica
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Uri Abraham, Stevo Todorčević (1997)
Fundamenta Mathematicae
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A combinatorial statement concerning ideals of countable subsets of ω is introduced and proved to be consistent with the Continuum Hypothesis. This statement implies the Suslin Hypothesis, that all (ω, ω*)-gaps are Hausdorff, and that every coherent sequence on ω either almost includes or is orthogonal to some uncountable subset of ω.
O. Alas, I. Protasov, M. Tkačenko, V. Tkachuk, R. Wilson, I. Yaschenko (1998)
Fundamenta Mathematicae
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We prove that any topological group of a non-measurable cardinality is hereditarily paracompact and strongly σ-discrete as soon as it is submaximal. Consequently, such a group is zero-dimensional. Examples of uncountable maximal separable spaces are constructed in ZFC.
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...
Umberto Zannier (1996)
Acta Arithmetica
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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 .
Daniel Coray, Constantin Manoil (1996)
Acta Arithmetica
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