TY - JOUR
T1 - Adding linear orders
AU - Shelah, Saharon
AU - Simon, Pierre
PY - 2012/6
Y1 - 2012/6
N2 - We address the following question: Can we expand an NIP theory by adding a linear order such that the expansion is still NIP? Easily, if acl(A)=A for all A, then this is true. Otherwise, we give counterexamples. More precisely, there is a totally categorical theory for which every expansion by a linear order has IP. There is also an ω-stable NDOP theory for which every expansion by a linear order interprets pseudofinite arithmetic.
AB - We address the following question: Can we expand an NIP theory by adding a linear order such that the expansion is still NIP? Easily, if acl(A)=A for all A, then this is true. Otherwise, we give counterexamples. More precisely, there is a totally categorical theory for which every expansion by a linear order has IP. There is also an ω-stable NDOP theory for which every expansion by a linear order interprets pseudofinite arithmetic.
UR - http://www.scopus.com/inward/record.url?scp=84862530251&partnerID=8YFLogxK
U2 - 10.2178/jsl/1333566647
DO - 10.2178/jsl/1333566647
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:84862530251
SN - 0022-4812
VL - 77
SP - 717
EP - 725
JO - Journal of Symbolic Logic
JF - Journal of Symbolic Logic
IS - 2
ER -