Explicit 4-descents on an elliptic curve
J. R. Merriman, S. Siksek, N. P. Smart (1996)
Acta Arithmetica
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J. R. Merriman, S. Siksek, N. P. Smart (1996)
Acta Arithmetica
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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
E. V. Flynn, N. P. Smart (1997)
Acta Arithmetica
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Umberto Zannier (1995)
Acta Arithmetica
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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...
Alan Dow, Klaas Hart (2000)
Fundamenta Mathematicae
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The Open Colouring Axiom implies that the measure algebra cannot be embedded into P(ℕ)/fin. We also discuss errors in previous results on the embeddability of the measure algebra.