TY - JOUR
T1 - A dichotomy theorem for regular types
AU - Hrushovski, Ehud
AU - Shelah, Saharon
PY - 1989/12/12
Y1 - 1989/12/12
N2 - Theorem 1.(a) LetT be a superstable theory without the omitting type order property. Then every regular type is either locally modular, or non-orthogonal to a strongly regular type. In the latter case, a realization of the strongly regular type can be found algebraically in any realization of the given one.(b) LetT be a superstable theory with NOTOP and NDOP. Then every regular type is either locally modular or strongly regular.Theorem 2.(a) Letp be a nontrivial regular type. Thenp-weight is continuous and definable inside some definable setD of positivep-weight. Ifp is non-orthogonal toB, thenD can be chosen definable overB.(b) Letp be a nontrivial regular type of depth 0. Let stp(a/B) bep-semi-regular. Thena lies in some acl(B)-definable setD such thatp-weight is continuousand definable insideD.
AB - Theorem 1.(a) LetT be a superstable theory without the omitting type order property. Then every regular type is either locally modular, or non-orthogonal to a strongly regular type. In the latter case, a realization of the strongly regular type can be found algebraically in any realization of the given one.(b) LetT be a superstable theory with NOTOP and NDOP. Then every regular type is either locally modular or strongly regular.Theorem 2.(a) Letp be a nontrivial regular type. Thenp-weight is continuous and definable inside some definable setD of positivep-weight. Ifp is non-orthogonal toB, thenD can be chosen definable overB.(b) Letp be a nontrivial regular type of depth 0. Let stp(a/B) bep-semi-regular. Thena lies in some acl(B)-definable setD such thatp-weight is continuousand definable insideD.
UR - http://www.scopus.com/inward/record.url?scp=0039802303&partnerID=8YFLogxK
U2 - 10.1016/0168-0072(89)90059-6
DO - 10.1016/0168-0072(89)90059-6
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:0039802303
SN - 0168-0072
VL - 45
SP - 157
EP - 169
JO - Annals of Pure and Applied Logic
JF - Annals of Pure and Applied Logic
IS - 2 PART 1
ER -