A semantic construction of two-ary integers

To binary trees, two-ary integers are what usual integers are to natural numbers, seen as unary trees. We can represent two-ary integers as binary trees too, yet with leaves labelled by binary words and with a structural restriction. In a sense, they are simpler than the binary trees, they relativize. Hence, contrary to the extensions known from Arithmetic and Algebra, this integer extension does not make the starting objects more complex. We use a semantic construction to get this extension. This method difiers from the algebraic ones, mainly because it is able to flnd equational features of the extended objects. Two-ary integers turn out to