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Arithmetic Formulated Relevantly
2021
The Australasian Journal of Logic
The purpose of this paper is to formulate first-order Peano arithmetic within the resources of relevant logic, and to demonstrate certain properties of the system thus formulated. Striking among these properties are the facts that (1) it is trivial that relevant arithmetic is absolutely consistent, but (2) classical first-order Peano arithmetic is straightforwardly contained in relevant arithmetic. Under (1), I shall show in particular that 0 = 1 is a non-theorem of relevant arithmetic; this,
doi:10.26686/ajl.v18i5.6905
fatcat:3uedkjs4tzfkfeghvr5y4qbski