论文信息 - Making the Hyperreal Line Both Saturated and Complete

Making the Hyperreal Line Both Saturated and Complete

In a nonstandard universe, the K-saturation property states that any family of fewer than K internal sets with the finite intersection property has a nonempty intersection. An ordered field F is said to have the A-Bolzano-Weierstrass property iff F has cofinality A and every bounded A-sequence in F has a convergent A-subsequence. We show that if K < A are uncountable regular cardinals and fl, < A whenever a < K and /1 < A, then there is a K-saturated nonstandard universe in which the hyperreal numbers have the A-Bolzano-Weierstrass property. The result also applies to certain fragments of set theory and second

H. Jerome Keisler | James H. Schmerl | H. Keisler | J. Schmerl

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