Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

There’s no forcing a least upper bound
HTML articles powered by AMS MathViewer

by Robert S. Lubarsky PDF
Proc. Amer. Math. Soc. 105 (1989), 998-1002 Request permission

Abstract:

While it is possible to have an increasing $\omega$-sequence of $c$-degrees with a least upper bound in a particular model of ZF, we show that it is not possible to force a sequence with a least upper bound absolute among all generic extensions of the original model
References
  • J. Truss, A note on increasing sequences of constructibility degrees, Higher set theory (Proc. Conf., Math. Forschungsinst., Oberwolfach, 1977) Lecture Notes in Math., vol. 669, Springer, Berlin, 1978, pp. 473–476. MR 520202
  • Thomas Jech, Set theory, Pure and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 506523
  • Ronald B. Jensen and Håvard Johnsbråten, A new construction of a non-constructible $\Delta _{3}^{1}$ subset of $\omega$, Fund. Math. 81 (1974), 279–290. MR 419229, DOI 10.4064/fm-81-4-279-290
  • Robert S. Lubarsky, Sacks forcing sometimes needs help to produce a minimal upper bound, J. Symbolic Logic 54 (1989), no. 2, 490–498. MR 997882, DOI 10.2307/2274863
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 03E40, 03E45
  • Retrieve articles in all journals with MSC: 03E40, 03E45
Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 105 (1989), 998-1002
  • MSC: Primary 03E40; Secondary 03E45
  • DOI: https://doi.org/10.1090/S0002-9939-1989-0943796-8
  • MathSciNet review: 943796