@article{Bac:Rog:Vij:95,
author = {Backofen, Rolf and Rogers, James and Vijay-Shanker, K.},
title = {A First-Order Axiomatization of the Theory of Finite Trees},
journal = {Journal of Logic, Language and Information},
year = {1995},
doi = {https://www.jstor.org/stable/40180058},
volume = {4},
pages = {5-39},
number = {1},
abstract = {We provide first-order  axioms for  the theories  of  finite trees  with
            bounded branching  and finite trees  with arbitrary  (finite) branching.
            The  signature is chosen to express,  in a natural way, those properties
            of trees most  relevant to  linguistic theories.  These axioms provide a
            foundation for  results  in linguistics  that  are  based  on  reasoning
            formally about  such  properties.  We include  some  observations on the
            expressive power of  these  theories  relative  to traditional  language
            complexity classes.}
}