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Displaying similar documents to “When ℵ₁ many sets are contained in a countably generated σ-field”

An uncountable partition contained in the atomless σ-field

Radosław Drabiński (2011)

Colloquium Mathematicae

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This short note considers the question of whether every atomless σ-field contains an uncountable partition. The paper comments the situation for a couple of known σ-fields. A negative answer to the question is the main result.

On ruled fields

Jack Ohm (1989)

Journal de théorie des nombres de Bordeaux

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Some results and problems that arise in connection with the foundations of the theory of ruled and rational field extensions are discussed.

Triangulation in o-minimal fields with standard part map

Lou van den Dries, Jana Maříková (2010)

Fundamenta Mathematicae

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In answering questions of J. Maříková [Fund. Math. 209 (2010)] we prove a triangulation result that is of independent interest. In more detail, let R be an o-minimal field with a proper convex subring V, and let st: V → k be the corresponding standard part map. Under a mild assumption on (R,V) we show that a definable set X ⊆ Vⁿ admits a triangulation that induces a triangulation of its standard part st X ⊆ kⁿ.