On winning Ehrenfeucht games and monadic NP Original Research Article

Inexpressibility results in Finite Model Theory are often proved by showing that Duplicator, one of the two players of an Ehrenfeucht game, has a winning strategy on certain structures. In this article a new method is introduced that allows, under certain conditions, the extension of a winning strategy of Duplicator on some small parts of two finite structures to a global winning strategy. As applications of this technique it is shown that • — Graph Connectivity is not expressible in existential monadic second-order logic (MonNP), even in the presence of a built-in linear order, • — Graph Connectivity is not expressible in MonNP even in the presence of arbitrary built-in relations of degree n0(1), and • — the presence of a built-in linear order gives MonNP more expressive power than the presence of a built-in successor relation.