### On long EF-equivalence in non-isomorphic models

by Shelah. [Sh:836]

Proc Logic Colloquium, Helsinki, August 2003, 2006

There has been much interest on constructing models which are
not isomorphic of cardinality lambda but are equivalent under the
Ehrenfeucht--Fraisse game of length alpha even for every alpha <
lambda . So under G.C.H. we know much. We deal here with
constructions of such pairs of models proven in ZFC and get the
existence under mild conditions.

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