# 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 ordinalâ€“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)

Bib entry

@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} }