Upward Categoricity from a Successor Cardinal for Tame Abstract Classes with Amalgamation

Journal of Symbolic Logic 70 (2):639 - 660 (2005)
  Copy   BIBTEX


This paper is devoted to the proof of the following upward categoricity theorem: Let K be a tame abstract elementary class with amalgamation, arbitrarily large models, and countable Löwenheim-Skolem number. If K is categorical in ‮א‬₁ then K is categorical in every uncountable cardinal. More generally, we prove that if K is categorical in a successor cardinal λ⁺ then K is categorical everywhere above λ⁺



    Upload a copy of this work     Papers currently archived: 78,059

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Rich models.Michael H. Albert & Rami P. Grossberg - 1990 - Journal of Symbolic Logic 55 (3):1292-1298.
Notes on quasiminimality and excellence.John T. Baldwin - 2004 - Bulletin of Symbolic Logic 10 (3):334-366.


Added to PP

16 (#677,707)

6 months
1 (#486,551)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Tameness and extending frames.Will Boney - 2014 - Journal of Mathematical Logic 14 (2):1450007.
Abstract elementary classes stable in ℵ0.Saharon Shelah & Sebastien Vasey - 2018 - Annals of Pure and Applied Logic 169 (7):565-587.

View all 7 citations / Add more citations

References found in this work

Toward categoricity for classes with no maximal models.Saharon Shelah & Andrés Villaveces - 1999 - Annals of Pure and Applied Logic 97 (1-3):1-25.
Amalgamation properties and finite models in L n -theories.John Baldwin & Olivier Lessmann - 2002 - Archive for Mathematical Logic 41 (2):155-167.
Finite diagrams stable in power.Saharon Shelah - 1970 - Annals of Mathematical Logic 2 (1):69.

Add more references