Assumptions of infinity. (English) Zbl 1329.03021
Link, Godehard (ed.), Formalism and beyond. On the nature of mathematical discourse. Berlin: De Gruyter (ISBN 978-1-61451-829-7/hbk; 978-1-61451-847-1/ebook). Logos 23, 229-274 (2014).
The author offers a great variety of possible definitions for the fact that “(theory) \(T\) makes an assumption of infinity”, for “\(T\) assumes merely the finite”, and for “\(T\) assumes the potentially infinite” – both in the sense of “\(\alpha(x)\) expresses that \(x\) is infinite (or finite) relative to \(T\)”, and in the sense that every model of \(T\) has to be infinite (or finite) – and assesses their strengths and weaknesses, both inside various set-theoretical and inside mereological settings.
For the entire collection see [Zbl 1326.03008].
For the entire collection see [Zbl 1326.03008].
Reviewer: Victor V. Pambuccian (Phoenix)
MSC:
| 03A05 | Philosophical and critical aspects of logic and foundations |
| 03E47 | Other notions of set-theoretic definability |
