Categoricity of an abstract elementary class in two successive cardinals
Saharon Shelah
Abstract
We investigate categoricity of abstract elementary classes without any remnants of compactness (like non-definability of well ordering, existence of E.M. models or existence of large cardinals). We prove (assuming a weak version of GCH around lambda) that if K is categorical in lambda, lambda+, LS(K) <= lambda and 1 <= I(lambda++,K)< 2lambda++ then K has a model in lambda+++ .
Create a lesson
Related papers
The universal measure of nonstochastic objects
Vladimir Vovk
Hyperarithmetic directions can all be exceptional for Marstrand's projection theorem
Noam Greenberg, Daniel Turetsky
Open Problems in Mathematical Logic
George Barmpalias, Su Gao, Jialiang He et al.
An easy proof that there may be no P-points
David Chodounský, Osvaldo Guzmán, Jonathan Verner
Comments on Choiceless Chain Conditions
Constance Bromham, Asaf Karagila
Localic Esakia Duality via Conic Frames
Nesta van der Schaaf