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  1. The Craig Interpolation Theorem in abstract model theory.Jouko Väänänen - 2008 - Synthese 164 (3):401-420.
    The Craig Interpolation Theorem is intimately connected with the emergence of abstract logic and continues to be the driving force of the field. I will argue in this paper that the interpolation property is an important litmus test in abstract model theory for identifying “natural,” robust extensions of first order logic. My argument is supported by the observation that logics which satisfy the interpolation property usually also satisfy a Lindström type maximality theorem. Admittedly, the range of such logics is small.
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  • Almost free groups and long Ehrenfeucht–Fraı̈ssé games.Pauli Väisänen - 2003 - Annals of Pure and Applied Logic 123 (1-3):101-134.
    An Abelian group G is strongly λ -free iff G is L ∞, λ -equivalent to a free Abelian group iff the isomorphism player has a winning strategy in an Ehrenfeucht–Fraı̈ssé game of length ω between G and a free Abelian group. We study possible longer Ehrenfeucht–Fraı̈ssé games between a nonfree group and a free Abelian group. A group G is called ε -game-free if the isomorphism player has a winning strategy in an Ehrenfeucht–Fraı̈ssé game of length ε between G (...)
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  • Almost free groups and Ehrenfeucht–Fraı̈ssé games for successors of singular cardinals.Saharon Shelah & Pauli Väisänen - 2002 - Annals of Pure and Applied Logic 118 (1-2):147-173.
    We strengthen nonstructure theorems for almost free Abelian groups by studying long Ehrenfeucht–Fraı̈ssé games between a fixed group of cardinality λ and a free Abelian group. A group is called ε -game-free if the isomorphism player has a winning strategy in the game of length ε ∈ λ . We prove for a large set of successor cardinals λ = μ + the existence of nonfree -game-free groups of cardinality λ . We concentrate on successors of singular cardinals.
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