On n-equivalence of binary trees
The paper contains a simple characterization of the binary trees which satisfy the same first-order sentences of quantifier depth n as the binary tree with one root whose branches all have length m (for all n and m). It follows immediately that, e.g., ``finiteness'' is not a first- order property of binary trees. The proof employs the Ehrenfeucht game.
first-order sentences of quantifier depth n
scientific article; zbMATH DE number 4014683