Sh:E102
- Kolman, O., & Shelah, S. (2024). Categoricity and amalgamation for AEC, and \kappa measurable. Bol. Mat., 31(1), 44. arXiv: math/9602216 MR: 4955284
-
Abstract:
In the original version of this paper, we assume a theory T that the logic \mathbb L _{\kappa, \aleph_{0}} is categorical in a cardinal \lambda > \kappa, and \kappa is a measurable cardinal. There we prove that the class of model of T of cardinality <\lambda (but \geq |T|+\kappa) has the amalgamation property; this is a step toward understanding the character of such classes of models.In this revised version we replaced the class of models of T by \mathfrak k, an AEC (abstract elementary class) which has LS-number {<} \, \kappa, or at least which behave nicely for ultrapowers by D, a normal ultra-filter on \kappa.
Presently sub-section §1A deals with T \subseteq \mathbb L_{\kappa^{+}, \aleph_{0}} (and so does a large part of the introduction and little in the rest of §1), but otherwise, all is done in in the context of AEC.
- Version 2024-12-17_2 (37p)
Bib entry
@article{Sh:E102,
author = {Kolman, Oren and Shelah, Saharon},
title = {{Categoricity and amalgamation for AEC, and $\kappa$ measurable}},
journal = {Bol. Mat.},
fjournal = {Bolet\'{\i}n de Matem\'{a}ticas. Nueva Serie},
volume = {31},
number = {1},
year = {2024},
pages = {44},
issn = {0120-0380,2357-6529},
mrnumber = {4955284},
mrclass = {03C48 (03C45 03C55 03C75 03E05 03E55)},
note = {\href{https://arxiv.org/abs/math/9602216}{arXiv: math/9602216}},
arxiv_number = {math/9602216}
}