TY - JOUR
T1 - Independence, dimension and continuity in non-forking frames
AU - Jarden, Adi
AU - Sitton, Alon
PY - 2013/6
Y1 - 2013/6
N2 - The notion J is independent in (M,M0,N) was established by Shelah, for an AEC (abstract elementary class) which is stable in some cardinal ë and has a non-forking relation, satisfying the good ë-frame axioms and some additional hypotheses. Shelah uses independence to define dimension. Here, we show the connection between the continuity property and dimension: if a non-forking satisfies natural conditions and the continuity property, then the dimension is well-behaved. As a corollary, we weaken the stability hypothesis and two additional hypotheses, that appear in Shelah's theorem.
AB - The notion J is independent in (M,M0,N) was established by Shelah, for an AEC (abstract elementary class) which is stable in some cardinal ë and has a non-forking relation, satisfying the good ë-frame axioms and some additional hypotheses. Shelah uses independence to define dimension. Here, we show the connection between the continuity property and dimension: if a non-forking satisfies natural conditions and the continuity property, then the dimension is well-behaved. As a corollary, we weaken the stability hypothesis and two additional hypotheses, that appear in Shelah's theorem.
UR - http://www.scopus.com/inward/record.url?scp=84881343980&partnerID=8YFLogxK
U2 - 10.2178/jsl.7802140
DO - 10.2178/jsl.7802140
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AN - SCOPUS:84881343980
SN - 0022-4812
VL - 78
SP - 602
EP - 632
JO - Journal of Symbolic Logic
JF - Journal of Symbolic Logic
IS - 2
ER -