Book Review: Uncountably categorical theories
نویسندگان
چکیده
منابع مشابه
Constructive Models of Uncountably Categorical Theories
We construct a strongly minimal (and thus uncountably categorical) but not totally categorical theory in a nite language of binary predicates whose only constructive (or recursive) model is the prime model. 0. Introduction. E ective (or recursive) model theory studies to which degree constructions in model theory and algebra can be made e ective. A presentation of a countable model M is an isom...
متن کاملThe Structure of Models of Uncountably Categorical Theories
The natural notion of categoricity, as it was discovered in the 1930's, is degenerate for first order languages, since only a finite structure can be described up to isomorphism by its first order theory. This has led to a new notion of categoricity. A theory is said to be categorical in a power if it has a model of this power which is unique up to isomorphism. Morley has proved, answering the ...
متن کاملA New Uncountably Categorical Group
We construct an uncountably categorical group with a geometry that is not locally modular. It is not possible to interpret a field in this group. We show the group is CM-trivial.
متن کاملModel completeness for trivial, uncountably categorical theories of Morley rank 1
We use this theorem to derive the same corollaries for the theories covered by the theorem as were derived for the strongly minimal case in [2]. We also note that the theorem is in some senses optimal. Specifically we can easily construct trivial Morley Rank 1 theories which are not categorical and for which the conclusion of the theorem fails. Also Marker in [3] constructs trivial totally cate...
متن کاملModel Completeness for Trivial, Uncountably Categorical Theories of Morley Rank 1 Alfred Dolich, Michael C. Laskowski, and Alexander Raichev
We use this theorem to derive the same corollaries for the theories covered by the theorem as were derived for the strongly minimal case in [2]. We also note that the theorem is in some senses optimal. Specifically we can easily construct trivial Morley Rank 1 theories which are not categorical and for which the conclusion of the theorem fails. Also Marker in [3] constructs trivial totally cate...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1994
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1994-00473-2