Upward categoricity from a successor cardinal for tame abstract classes with amalgamation

Lessmann, Olivier

J. Symbolic Logic, Tome 70 (2005) no. 1, p. 639-660 / Harvested from Project Euclid

Résumé

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⁺.

Publié le : 2005-06-14
Classification:

@article{1120224733,
     author = {Lessmann, Olivier},
     title = {Upward categoricity from a successor cardinal for tame abstract classes with amalgamation},
     journal = {J. Symbolic Logic},
     volume = {70},
     number = {1},
     year = {2005},
     pages = { 639-660},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1120224733}
}

Lessmann, Olivier. Upward categoricity from a successor cardinal for tame abstract classes with amalgamation. J. Symbolic Logic, Tome 70 (2005) no. 1, pp.  639-660. http://gdmltest.u-ga.fr/item/1120224733/