Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Making the Hyperreal Line Both Saturated and Complete

H. Jerome Keisler and James H. Schmerl
The Journal of Symbolic Logic
Vol. 56, No. 3 (Sep., 1991), pp. 1016-1025
DOI: 10.2307/2275069
Stable URL: http://www.jstor.org/stable/2275069
Page Count: 10
  • Read Online (Free)
  • Download ($10.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Making the Hyperreal Line Both Saturated and Complete
Preview not available

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 $\kappa < \lambda$ are uncountable regular cardinals and $\beta^\alpha < \lambda$ whenever $\alpha < \kappa$ and $\beta < \lambda$, 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.

Page Thumbnails

  • Thumbnail: Page 
1016
    1016
  • Thumbnail: Page 
1017
    1017
  • Thumbnail: Page 
1018
    1018
  • Thumbnail: Page 
1019
    1019
  • Thumbnail: Page 
1020
    1020
  • Thumbnail: Page 
1021
    1021
  • Thumbnail: Page 
1022
    1022
  • Thumbnail: Page 
1023
    1023
  • Thumbnail: Page 
1024
    1024
  • Thumbnail: Page 
1025
    1025