Constructing ω-stable structures: Rank 2 fields

Journal of Symbolic Logic 65 (1):371-391 (2000)
  Copy   BIBTEX

Abstract

We provide a general framework for studying the expansion of strongly minimal sets by adding additional relations in the style of Hrushovski. We introduce a notion of separation of quantifiers which is a condition on the class of expansions of finitely generated models for the expanded theory to have a countable ω-saturated model. We apply these results to construct for each sufficiently fast growing finite-to-one function μ from 'primitive extensions' to the natural numbers a theory T μ of an expansion of an algebraically closed field which has Morley rank 2. Finally, we show that if μ is not finite-to-one the theory may not be ω-stable

Other Versions

No versions found

Links

PhilArchive

    This entry is not archived by us. If you are the author and have permission from the publisher, we recommend that you archive it. Many publishers automatically grant permission to authors to archive pre-prints. By uploading a copy of your work, you will enable us to better index it, making it easier to find.

    Upload a copy of this work     Papers currently archived: 102,589

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

Constructing ω-stable Structures: Rank k-fields.John T. Baldwin & Kitty Holland - 2003 - Notre Dame Journal of Formal Logic 44 (3):139-147.
Constructing ω-stable structures: model completeness.John T. Baldwin & Kitty Holland - 2004 - Annals of Pure and Applied Logic 125 (1-3):159-172.
On atomic or saturated sets.Ludomir Newelski - 1996 - Journal of Symbolic Logic 61 (1):318-333.
Interpreting structures of finite Morley rank in strongly minimal sets.Assaf Hasson - 2007 - Annals of Pure and Applied Logic 145 (1):96-114.
The geometry of forking and groups of finite Morley rank.Anand Pillay - 1995 - Journal of Symbolic Logic 60 (4):1251-1259.
The spectrum of resplendency.John T. Baldwin - 1990 - Journal of Symbolic Logic 55 (2):626-636.
On pseudolinearity and generic pairs.Evgueni Vassiliev - 2010 - Mathematical Logic Quarterly 56 (1):35-41.
Fusion over Sublanguages.Assaf Hasson & Martin Hils - 2006 - Journal of Symbolic Logic 71 (2):361 - 398.

Analytics

Added to PP
2009-01-28

Downloads
137 (#164,888)

6 months
16 (#176,141)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Citations of this work

Constructing ω-stable structures: model completeness.John T. Baldwin & Kitty Holland - 2004 - Annals of Pure and Applied Logic 125 (1-3):159-172.
Fusion over a vector space.Andreas Baudisch, Amador Martin-Pizarro & Martin Ziegler - 2006 - Journal of Mathematical Logic 6 (2):141-162.
Notes on quasiminimality and excellence.John T. Baldwin - 2004 - Bulletin of Symbolic Logic 10 (3):334-366.
Bi-colored expansions of geometric theories.S. Jalili, M. Pourmahdian & M. Khani - 2025 - Annals of Pure and Applied Logic 176 (2):103525.

View all 9 citations / Add more citations

References found in this work

A new strongly minimal set.Ehud Hrushovski - 1993 - Annals of Pure and Applied Logic 62 (2):147-166.
Stable generic structures.John T. Baldwin & Niandong Shi - 1996 - Annals of Pure and Applied Logic 79 (1):1-35.
Superstable groups.Ch Berline & D. Lascar - 1986 - Annals of Pure and Applied Logic 30 (1):1-43.
Superstable fields and groups.G. Cherlin - 1980 - Annals of Mathematical Logic 18 (3):227.
Strongly minimal fusions of vector spaces.Kitty L. Holland - 1997 - Annals of Pure and Applied Logic 83 (1):1-22.

View all 6 references / Add more references