## Theories with Ehrenfeucht-Fraïssé equivalent non-isomorphic models## Saharon Shelah
Our "long term and large scale" aim is to characterize the first order theories T (at least the countable ones)
such that for every ordinal
α there are
λ, M
_{1}, M_{2}
such that M_{1} and M_{2} are non-isomorphic
models of T
of cardinality λ which are
EF^{+} _{α,λ}-equivalent.
We expect that as in the
main gap [11, XII], we get a strong
dichotomy, i.e., on the non-structure side we have stronger, better
examples,
and on the structure side we have an analogue of [11, XIII]. We
presently prove
the consistency
of the non-structure side for T
which is χ_{0}-independent
(= not strongly dependent),
even for PC(T_{1},T).
Tbilisi Mathematical Journal, Vol. 1(2008), pp. 133-164 |