TY - JOUR
T1 - Dependent first order theories, continued
AU - Shelah, Saharon
PY - 2009/1
Y1 - 2009/1
N2 - A dependent theory is a (first order complete theory) T which does not have the independence property. A major result here is: if we expand a model of T by the traces on it of sets definable in a bigger model then we preserve its being dependent. Another one justifies the cofinality restriction in the theorem (from a previous work) saying that pairwise perpendicular indiscernible sequences, can have arbitrary dual-cofinalities in some models containing them. We introduce "strongly dependent" and look at definable groups; and also at dividing, forking and relatives.
AB - A dependent theory is a (first order complete theory) T which does not have the independence property. A major result here is: if we expand a model of T by the traces on it of sets definable in a bigger model then we preserve its being dependent. Another one justifies the cofinality restriction in the theorem (from a previous work) saying that pairwise perpendicular indiscernible sequences, can have arbitrary dual-cofinalities in some models containing them. We introduce "strongly dependent" and look at definable groups; and also at dividing, forking and relatives.
UR - http://www.scopus.com/inward/record.url?scp=71249122648&partnerID=8YFLogxK
U2 - 10.1007/s11856-009-0082-1
DO - 10.1007/s11856-009-0082-1
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AN - SCOPUS:71249122648
SN - 0021-2172
VL - 173
SP - 1
EP - 60
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -