A first-order axiomatization of the theory of finite trees

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
Keywords Trees  First-Order Theories  Axiomatizations  Natural Language Syntax  Ehrenfeucht-Fraïssé Games
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DOI 10.1007/BF01048403
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Kees Doets (1989). Monadic $\Pi^11$-Theories of $\Pi1^1$}-Properties. Notre Dame Journal of Formal Logic 30 (2):224-240.

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