Open AccessAlien Intruders in Relevant Arithmetic
Author(s) -
Robert K. Meyer,
Chris Mortensen
Publication year - 2021
Publication title -
australasian journal of logic
Language(s) - English
Resource type - Journals
ISSN - 1448-5052
DOI - 10.26686/ajl.v18i5.6910
Subject(s) - arithmetic , natural number , natural (archaeology) , mathematics , rational number , algebra over a field , alien , discrete mathematics , computer science , pure mathematics , geography , sociology , population , demography , archaeology , census
This paper explores the model theory of relevant arithmetic, emphasizing the structure of nonstandard natural numbers in the relevant arithmetic R#. In particular, the authors prove the “Alien Intruder Theorem” guaranteeing the existence of a model of R# including the rational numbers in which each rational acts as a nonstandard natural number. The authors conclude by considering some consequences of and open questions about the construction used in the theorem.