Structural Equivalence of Arithmetical Expressions as a Technical Basis for Philosophical Arithmetic

The word “fracterm” is a portmanteau of “fraction” and “term.” Fracterms are instances of arithmetical terms, A-terms, for short. Four notions of correspondence for A-terms are distinguished: syntactic equality, structural equivalence, semantic equivalence (having the same value), and frugal equality. We provide axioms for structural equivalence and discuss the connection with semantic equivalence and frugal equality.