# Sh:560

• Laskowski, M. C., & Shelah, S. (2001). The Karp complexity of unstable classes. Arch. Math. Logic, 40(2), 69–88.
• 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 the class of doubly transitive linear orders is controlled, while any pseudo-elementary class with the \omega-independence property is not controlled.
• Version 2000-10-31_10 (24p) published version (20p)
Bib entry
@article{Sh:560,
author = {Laskowski, Michael Chris and Shelah, Saharon},
title = {{The Karp complexity of unstable classes}},
journal = {Arch. Math. Logic},
fjournal = {Archive for Mathematical Logic},
volume = {40},
number = {2},
year = {2001},
pages = {69--88},
issn = {0933-5846},
mrnumber = {1816478},
mrclass = {03C45 (03C75)},
doi = {10.1007/s001530000047},
note = {\href{https://arxiv.org/abs/math/0011167}{arXiv: math/0011167}},
arxiv_number = {math/0011167}
}