Canonical bases in excellent classes
نویسندگان
چکیده
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 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.
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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...
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The dual basis of the canonical basis of the modified quantized enveloping algebra is studied, in particular for type A. The construction of a basis for the coordinate algebra of the n × n quantum matrices is appropriate for the study the multiplicative property. It is shown that this basis is invariant under multiplication by certain quantum minors including the quantum determinant. Then a bas...
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Inflectional classes are a basic notion in morphology, though occasionally their existence is challenged. In trying to get a new perspective on complex phenomena, like inflectional classes, we may take a ‘canonical’ approach. This means that we extrapolate from what there is to what there might be, in order to define the theoretical space. Within that scheme of theoretical possibilities we can ...
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ژورنال
عنوان ژورنال: Journal of Symbolic Logic
سال: 2008
ISSN: 0022-4812,1943-5886
DOI: 10.2178/jsl/1208358747