منابع مشابه
Categoricity, Amalgamation, and Tameness
Theorem. For each 2 ≤ k < ω there is an Lω1,ω-sentence φk such that: (1) φk is categorical in μ if μ ≤ אk−2; (2) φk is not אk−2-Galois stable; (3) φk is not categorical in any μ with μ > אk−2; (4) φk has the disjoint amalgamation property; (5) For k > 2, (a) φk is (א0,אk−3)-tame; indeed, syntactic first-order types determine Galois types over models of cardinality at most אk−3; (b) φk is אm-Gal...
متن کاملAmalgamation, Absoluteness, and Categoricity
We describe the major result on categoricity in Lω1,ω , placing it in the context of more general work in abstract elementary classes. In particular, we illustrate the role of higher dimensional amalgamations and sketch the role of a weak extension of ZFC in the proof. We expound the translation of the problem to studying atomic models of first order theories. We provide a simple example of the...
متن کاملCategoricity for Abstract Classes with Amalgamation Sh394
Let K be an abstract elementary class with amalgamation, and Lowenheim Skolem number LS(K). We prove that for a suitable Hanf number χ0 if χ0 < λ0 ≤ λ1, and K is categorical in λ + 1 then it is categorical in λ0. 2000 Mathematics Subject Classification. 03C45, 03C75.
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 کاملTameness and Extending Frames
We combine two notions in AECs, tameness and good λ-frames, and show that they together give a very well-behaved nonforking notion in all cardinalities. This helps to fill a longstanding gap in classification theory of tame AECs and increases the applicability of frames. Along the way, we prove a complete stability transfer theorem and uniqueness of limit models in these AECs.
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2009
ISSN: 0021-2172,1565-8511
DOI: 10.1007/s11856-009-0035-8