Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

$ 2\sp {2\sp \omega}$ nonisomorphic short ordered commutative domains whose quotient fields are long


Author: Krzysztof Ciesielski
Journal: Proc. Amer. Math. Soc. 113 (1991), 217-227
MSC: Primary 03E05; Secondary 03E75, 06F25, 12J15
MathSciNet review: 1079888
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A linearly ordered set is short if it does not contain any monotonic sequence of length $ {\omega _1}$, and it is long if it contains a monotonic sequence of length $ \alpha $ for every ordinal $ \alpha < {({2^\omega })^ + }$. We prove that there exists a family $ {\mathbf{F}}$ of power $ {2^{{2^\omega }}}$ of long ordered fields of size $ {2^\omega }$ that are pairwise nonisomorphic (as fields) and such that every field $ F \in {\mathbf{F}}$ has $ {2^{{2^\omega }}}$ nonisomorphic short subdomains whose field of quotients is $ F$. The generalization of this result for higher cardinals is also discussed. This generalizes the author's result of [Ci].


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 03E05, 03E75, 06F25, 12J15

Retrieve articles in all journals with MSC: 03E05, 03E75, 06F25, 12J15


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1079888-4
PII: S 0002-9939(1991)1079888-4
Keywords: Nonisomorphic, ordered commutative domains, quotient fields
Article copyright: © Copyright 1991 American Mathematical Society