Sh:259

• Grossberg, R. P., & Shelah, S. On Hanf numbers of the infinitary order property. Preprint. arXiv: math/9809196
• Abstract:
  We study several cardinal, and ordinal–valued functions that are relatives of Hanf numbers. Let $\kappa$ be an infinite cardinal, and let $T\subseteq L_{\kappa^+,\omega}$ be a theory of cardinality $\leq\kappa$, and let $\gamma$ be an ordinal $\geq\kappa^+$. For example we look at (1) $\mu_{T}^*(\gamma,\kappa):=\min\{\mu^*\forall\phi\in L_{\infty,\omega}$, with $rk(\phi)<\gamma$, if $T$ has the $(\phi,\mu^*)$-order property then there exists a formula $\phi'(x;y)\in L_{\kappa^+,\omega}$, such that for every $\chi\geq\kappa$, $T$ has the $(\phi',\chi)$-order property$\}$; and (2) $\mu^*(\gamma,\kappa):=\sup\{\mu_{T}^*(\gamma,\kappa)\;|\;T\in L_{\kappa^+,\omega}\}$.
• Version 1998-09-24_11 (23p)

@article{Sh:259,
 author = {Grossberg, Rami P. and Shelah, Saharon},
 title = {{On Hanf numbers of the infinitary order property}},
 note = {\href{https://arxiv.org/abs/math/9809196}{arXiv: math/9809196}},
 arxiv_number = {math/9809196}
}