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. arXiv: math/0303345 DOI: 10.1016/S0168-0072(02)00080-5 MR: 1949710
• 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.
• Version 2002-10-03_10 (24p) published version (21p)

@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},
 mrnumber = {1949710},
 mrclass = {03C45 (03C75)},
 doi = {10.1016/S0168-0072(02)00080-5},
 note = {\href{https://arxiv.org/abs/math/0303345}{arXiv: math/0303345}},
 arxiv_number = {math/0303345}
}