Large Finite Structures with Few Lk-Types

Abstract

For each k 3, we show that there is no recursive bound for the size of the smallest finite model of an Lk-theory in terms of its k-size. Here Lk denotes the k-variable fragment of first-order logic. An Lk-theory is a maximal consistent set of Lk-sentences, and the k-size of an Lk-theory is the number of Lk-types realized in its models. Our result answers a… (More)
DOI: 10.1109/LICS.1997.614949

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