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Making the hyperreal line both saturated and complete

  • H. Jerome Keisler (a1) and James H. Schmerl (a2)

Abstract

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

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Making the hyperreal line both saturated and complete

  • H. Jerome Keisler (a1) and James H. Schmerl (a2)

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