Australasian Journal of Logic 18 (5):524-568 (2021)

Shay Logan
Kansas State University
Graham Leach-Krouse
Kansas State University
In this paper we introduce a novel way of building arithmetics whose background logic is R. The purpose of doing this is to point in the direction of a novel family of systems that could be candidates for being the infamous R#1/2 that Meyer suggested we look for.
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References found in this work BETA

The Euclidean Diagram.Kenneth Manders - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford University Press. pp. 80--133.
Introduction to Higher Order Categorical Logic.J. Lambek & P. J. Scott - 1989 - Journal of Symbolic Logic 54 (3):1113-1114.
Adjointness in Foundations.F. William Lawvere - 1969 - Dialectica 23 (3‐4):281-296.
The Algebra of Intensional Logics.Jon Michael Dunn - 1966 - Dissertation, University of Pittsburgh

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