### Theories with EF-Equivalent Non-Isomorphic Models

by Shelah. [Sh:897]

Tbilisi Math J, 2008

Our ``large scale'' aim is to characterize the first order T
(at least the countable ones) such that: for every ordinal alpha
there lambda,M_1,M_2 such that M_1,M_2 are non-isomorphic
models of T of cardinality lambda which are
EF_{alpha, lambda}-equivalent. We expect that as in the main gap
([Sh:c,XII]) we get a strong dichotomy, so in the non-structure side
we have more, better example, and in the structure side we have a
parallel of [Sh:c,XIII]. We presently prove the consistency of the
non-structure side for T which is aleph_0-independent (= not
strongly dependent) or just not strongly stable, even for
PC (T_1,T) and more for unstable T (see [Sh:c,VII] or [Sh:h]) and
infinite linear order I .

Back to the list of publications