Categoricity John Baldwin February 3 , 2008
نویسنده
چکیده
Elementary Classes
منابع مشابه
Abstract Elementary Classes Motivations and Directions
Elementary Classes Motivations and Directions John T. Baldwin Why AEC? Categoricity and Complex Exponentiation Excellence– Generalized Amalgamation Eventual Categoricity Core Mathematics again Abstract Elementary Classes Motivations and Directions
متن کاملThe Lazy Model Theoretician’s Guide to Shelah’s Eventual Categoricity Conjecture in Universal Classes
We give a short overview of the proof of Shelah’s eventual categoricity conjecture in universal classes with amalgamation [Vasd].
متن کاملCompleteness and Categoricity (in power): Formalization without Foundationalism
We propose a criterion to regard a property of a theory (in first or second order logic) as virtuous: the property must have significant mathematical consequences for the theory (or its models). We then rehearse results of Ajtai, Marek, Magidor, H. Friedman and Solovay to argue that for second order logic, ‘categoricity’ has little virtue. For first order logic, categoricity is trivial; but ‘ca...
متن کاملCategoricity and Stability in Abstract Elementary Classes
Categoricity and Stability in Abstract Elementary Classes byMonica M. VanDieren This thesis tackles the classification theory of non-elementary classes from twoperspectives. In Chapter II we work towards a categoricity transfer theorem, whileChapter III focuses on the development of a stability theory for abstract elementaryclasses (AECs).The results in Chapter II are in a c...
متن کاملUncountable categoricity of local abstract elementary classes with amalgamation
We give a complete and elementary proof of the following upward categoricity theorem: LetK be a local abstract elementary class with amalgamation and joint embedding, arbitrarily large models, and countable LöwenheimSkolem number. If K is categorical in א1 then K is categorical in every uncountable cardinal. In particular, this provides a new proof of the upward part of Morley’s theorem in firs...
متن کامل