# Sh:687

• Laskowski, M. C., & Shelah, S. (2003). Karp complexity and classes with the independence property. Ann. Pure Appl. Logic, 120(1-3), 263–283.
• Abstract:
A class {\bf K} of structures is controlled if for all cardinals \lambda, the relation of L_{\infty,\lambda}-equivalence partitions {\bf K} into a set of equivalence classes (as opposed to a proper class). We prove that no pseudo-elementary class with the independence property is controlled. By contrast, there is a pseudo-elementary class with the strict order property that is controlled.
• published version (21p)
Bib entry
@article{Sh:687,
author = {Laskowski, Michael Chris and Shelah, Saharon},
title = {{Karp complexity and classes with the independence property}},
journal = {Ann. Pure Appl. Logic},
fjournal = {Annals of Pure and Applied Logic},
volume = {120},
number = {1-3},
year = {2003},
pages = {263--283},
issn = {0168-0072},
doi = {10.1016/S0168-0072(02)00080-5},
mrclass = {03C45 (03C75)},
mrnumber = {1949710},
mrreviewer = {U. Felgner},
doi = {10.1016/S0168-0072(02)00080-5},
note = {\href{https://arxiv.org/abs/math/0303345}{arXiv: math/0303345}},
arxiv_number = {math/0303345}
}