An Algebraic Generalization of Frege Structures-Binding Algebras
Abstract This paper introduces a kind of second-order algebras, called binding algebras , which is an algebraic generalization of Aczel's (1980) Frege structure. It investigates the universal property of binding algebras by following Birkhoff's (1935) method. An equational logic eBA is introduced. We obtain its admissible completeness. The relationship between completeness and the admissible completeness is very close and will be discussed.