Sh:1238

• Shelah, S. MODIFIED AECS FOR STRICTLY STABLE THEORIES. Preprint. arXiv: 2305.02020
• Abstract:
  Good frames were suggested in [Sh:h] as the bare-bones parallel, in the context of AECs, to superstable (among elementary classes). Here we consider (\mu,\lambda,\kappa)-frames as candidates for being (in the context of AECs) the correct parallel to the class of |T|^+-saturated models of a strictly stable (complete first-order) theory among elementary classes (we call them DAECs; directed AECs).

  One thing we lose compared to the superstable case is that going up by induction on cardinals is problematic (because of stages of small cofinality). But this arises only when we try to lift such classes to higher cardinals. Also, we may assume (as a replacement) the existence of prime models over unions of increasing chains.

• Version 2025-01-15_2 (38p)

@article{Sh:1238,
 author = {Shelah, Saharon},
 title = {{MODIFIED AECS FOR STRICTLY STABLE THEORIES}},
 note = {\href{https://arxiv.org/abs/2305.02020}{arXiv: 2305.02020}},
 arxiv_number = {2305.02020}
}