Sh:E102

• Kolman, O., & Shelah, S. Categoricity and amalgamation for AEC and \kappa measurable. Preprint. arXiv: math/9602216
• 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 2024-03-03 (37p)

@article{Sh:E102,
 author = {Kolman, Oren and Shelah, Saharon},
 title = {{Categoricity and amalgamation for AEC and $ \kappa $ measurable}},
 note = {\href{https://arxiv.org/abs/math/9602216}{arXiv: math/9602216}},
 arxiv_number = {math/9602216}
}