@inbook{954e5c0eae7241caad66e55510b5256a,
title = "Relevant Rational Arithmetic",
abstract = "The arithmetic R♯ is obtained by postulating the Peano axioms on the basis of the relevant logic R. R♯ is a remarkable arithmetic, not least in that it has finite models. In this paper we examine the options for extending R♯ from natural numbers to rational numbers, as this is the essential next step towards providing a relevant basis for mathematics and for applications. Relevant rational number theory is problematic in that the most obvious approaches lead to non-conservative extensions of R♯. We consider three ways in which relevant theories of rational arithmetic can be formulated, and note in particular how these fare in the finite models of R♯.",
author = "John Slaney",
note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.",
year = "2024",
doi = "10.1007/978-3-031-69940-5_18",
language = "English",
series = "Trends in Logic",
publisher = "Springer Science and Business Media B.V.",
pages = "453--468",
booktitle = "Trends in Logic",
address = "Germany",
}