Displaying similar documents to “An uncountable partition contained in the atomless σ-field”

Extending automorphisms to the rational fractions field.

Fernando Fernández Rodríguez, Agustín Llerena Achutegui (1991)

Extracta Mathematicae

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We say that a field K has the Extension Property if every automorphism of K(X) extends to an automorphism of K. J.M. Gamboa and T. Recio [2] have introduced this concept, naive in appearance, because of its crucial role in the study of homogeneity conditions in spaces of orderings of functions fields. Gamboa [1] has studied several classes of fields with this property: Algebraic extensions of the field Q of rational numbers; euclidean, algebraically closed and pythagorean fields; fields...

When ℵ₁ many sets are contained in a countably generated σ-field

R. Drabiński, E. Grzegorek (2009)

Colloquium Mathematicae

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We discuss the problem when ℵ₁ sets are contained in a σ-generated σ-field on some set X. This is related to a problem raised by K. P. S. Bhaskara Rao and Rae Michael Shortt [Dissertationes Math. 372 (1998)] which we answer. We also briefly discuss generating the family of all subsets from rectangles.