منابع مشابه
On quasiminimal excellent classes
A careful exposition of Zilber’s quasiminimal excellent classes and their categoricity is given, leading to two new results: the Lω1,ω(Q)definability assumption may be dropped, and each class is determined by its model of dimension א0. Boris Zilber developed quasiminimal excellent classes in [Zil05], in order to prove that his conjectural description of complex exponentiation was categorical. T...
متن کاملQuasiminimal abstract elementary classes
We propose the notion of a quasiminimal abstract elementary class (AEC). This is an AEC satisfying four semantic conditions: countable Löwenheim-Skolem-Tarski number, existence of a prime model, closure under intersections, and uniqueness of the generic orbital type over every countable model. We exhibit a correspondence between Zilber’s quasiminimal pregeometry classes and quasiminimal AECs: a...
متن کاملAn Introduction to Excellent Classes
In this paper, we present Shelah’s theory of excellence concluding with his categoricity theorem for the class of atomic models of a countable first order theory, under the assumption that there exists a large full model. This allows us to do the entire work within ZFC and without any assumption on the number of models of size א1, in contrast to Shelah’s original treatment.
متن کاملCategoricity and U-rank in excellent classes
Let K be the class of atomic models of a countable first order theory. We prove that ifK is excellent and categorical in some uncountable cardinal, then each model is prime and minimal over the basis of a definable pregeometry given by a quasiminimal set. This implies thatK is categorical in all uncountable cardinals. We also introduce a U-rank to measure the complexity of complete types over m...
متن کاملExcellent Abstract Elementary Classes Are Tame
The assumption that an AEC is tame is a powerful assumption permitting development of stability theory for AECs with the amalgamation property. Lately several upward categoricity theorems were discovered where tameness replaces strong set-theoretic assumptions. We present in this article two sufficient conditions for tameness, both in form of strong amalgamation properties that occur in nature....
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ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 2010
ISSN: 0022-4812,1943-5886
DOI: 10.2178/jsl/1268917494