Constructing $\omega$-Stable Structures: Rank 2 Fields
Baldwin, John T. ; Holland, Kitty
J. Symbolic Logic, Tome 65 (2000) no. 1, p. 371-391 / Harvested from Project Euclid
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 $\omega$-saturated model. We apply these results to construct for each sufficiently fast growing finite-to-one function $\mu$ from 'primitive extensions' to the natural numbers a theory T$^\mu$ of an expansion of an algebraically closed field which has Morley rank 2. Finally, we show that if $\mu$ is not finite-to-one the theory may not be $\omega$-stable.
Publié le : 2000-03-14
Classification: 
@article{1183746028,
     author = {Baldwin, John T. and Holland, Kitty},
     title = {Constructing $\omega$-Stable Structures: Rank 2 Fields},
     journal = {J. Symbolic Logic},
     volume = {65},
     number = {1},
     year = {2000},
     pages = { 371-391},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183746028}
}
Baldwin, John T.; Holland, Kitty. Constructing $\omega$-Stable Structures: Rank 2 Fields. J. Symbolic Logic, Tome 65 (2000) no. 1, pp.  371-391. http://gdmltest.u-ga.fr/item/1183746028/