Geodesic
A semantic construction of two-ary integers
Discussiones Mathematicae. General Algebra and Applications, Tome 25 (2005) no. 2, pp. 165-219

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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.
Keywords: universal matrix, analytic monoid, LISP, semantics, jump 
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Ricci, Gabriele. A semantic construction of two-ary integers. Discussiones Mathematicae. General Algebra and Applications, Tome 25 (2005) no. 2, pp. 165-219. http://geodesic.mathdoc.fr/item/DMGAA_2005_25_2_a3/