On the strong Martin conjecture

Journal of Symbolic Logic 56 (3):862-875 (1991)
  Copy   BIBTEX


We study the following conjecture. Conjecture. Let T be an ω-stable theory with continuum many countable models. Then either i) T has continuum many complete extensions in L1(T), or ii) some complete extension of T in L1 has continuum many L1-types without parameters. By Shelah's proof of Vaught's conjecture for ω-stable theories, we know that there are seven types of ω-stable theory with continuum many countable models. We show that the conjecture is true for all but one of these seven cases. In the last case we show the existence of continuum many L2-types



    Upload a copy of this work     Papers currently archived: 91,219

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Determinateness of certain almost-borel games.Robert S. Wolf - 1985 - Journal of Symbolic Logic 50 (3):569-579.
Kueker's conjecture for stable theories.Ehud Hrushovski - 1989 - Journal of Symbolic Logic 54 (1):207-220.
The classification of small weakly minimal sets. II.Steven Buechler - 1988 - Journal of Symbolic Logic 53 (2):625-635.
A remark on Martin's conjecture.Su Gao - 2001 - Journal of Symbolic Logic 66 (1):401-406.
A refutation of pure conjecture.Timothy Cleveland - 1997 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 28 (1):55-81.
An information continuum conjecture.Ken Herold - 2003 - Minds and Machines 13 (4):553-566.
Vaught's conjecture for modules over a serial ring.Vera Puninskaya - 2000 - Journal of Symbolic Logic 65 (1):155-163.


Added to PP

52 (#294,915)

6 months
7 (#364,455)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.
Classification Theory and the Number of Nonisomorphic Models.S. Shelah - 1982 - Journal of Symbolic Logic 47 (3):694-696.
An Introduction to Stability Theory.Anand Pillay - 1986 - Journal of Symbolic Logic 51 (2):465-467.
On Martin's conjecture.C. M. Wagner - 1982 - Annals of Mathematical Logic 22 (1):47.

Add more references