# Sh:560

- Laskowski, M. C., & Shelah, S. (2001).
*The Karp complexity of unstable classes*. Arch. Math. Logic,**40**(2), 69–88. arXiv: math/0011167 DOI: 10.1007/s001530000047 MR: 1816478 -
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. - 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}, doi = {10.1007/s001530000047}, mrclass = {03C45 (03C75)}, mrnumber = {1816478}, mrreviewer = {U. Felgner}, doi = {10.1007/s001530000047}, note = {\href{https://arxiv.org/abs/math/0011167}{arXiv: math/0011167}}, arxiv_number = {math/0011167} }