The Karp complexity of unstable classes

Citation
Mc. Laskowski et S. Shelah, The Karp complexity of unstable classes, ARCH MATH L, 40(2), 2001, pp. 69-88
Citations number
13
Categorie Soggetti
Mathematics
Journal title
ARCHIVE FOR MATHEMATICAL LOGIC
ISSN journal
09335846 → ACNP
Volume
40
Issue
2
Year of publication
2001
Pages
69 - 88
Database
ISI
SICI code
0933-5846(200102)40:2<69:TKCOUC>2.0.ZU;2-2
Abstract
A class K of structures is controlled if, for all cardinals lambda, the rel ation of L-infinity.lambda-, equivalence partitions K into a set of equival ence classes (as opposed to a proper class). We prove that the class of dou bly transitive linear orders is controlled, while any pseudo-elementary cla ss with the omega -independence property is not controlled.