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- W2112149503 abstract "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 β α < 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." @default.
- W2112149503 created "2016-06-24" @default.
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- W2112149503 date "1991-09-01" @default.
- W2112149503 modified "2023-09-23" @default.
- W2112149503 title "Making the hyperreal line both saturated and complete" @default.
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- W2112149503 doi "https://doi.org/10.2307/2275069" @default.
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