TY - JOUR
T1 - Karp complexity and classes with the independence property
AU - Laskowski, M. C.
AU - Shelah, S.
PY - 2003/4/15
Y1 - 2003/4/15
N2 - A class K of structures is controlled if for all cardinals λ, the relation of L∞,λ-equivalence partitions 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 (see Arch. Math. Logic 40 (2001) 69-88).
AB - A class K of structures is controlled if for all cardinals λ, the relation of L∞,λ-equivalence partitions 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 (see Arch. Math. Logic 40 (2001) 69-88).
KW - Coding graphs
KW - Independence property
KW - Non-structure theorems
UR - http://www.scopus.com/inward/record.url?scp=0037445579&partnerID=8YFLogxK
U2 - 10.1016/S0168-0072(02)00080-5
DO - 10.1016/S0168-0072(02)00080-5
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AN - SCOPUS:0037445579
SN - 0168-0072
VL - 120
SP - 263
EP - 283
JO - Annals of Pure and Applied Logic
JF - Annals of Pure and Applied Logic
IS - 1-3
ER -