Abstract
Local Constructive Set Theory (LCST) is intended to be a local version of constructive set theory (CST). Constructive Set Theory is an open-ended set theoretical setting for constructive mathematics that is not committed to any particular brand of constructive mathematics and, by avoiding any built-in choice principles, is also acceptable in topos mathematics, the mathematics that can be carried out in an arbitrary topos with a natural numbers object.
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Notes
- 1.
That is a set that has an element and is such that it is a subset of its powerset.
- 2.
Free occurrences of x in Ï• become bound in \(\{ x\mid\phi\}\).
References
Aczel, P. (2006) Aspects of General Topology in Constructive Set Theory, Annals of Pure and Applied Logic, 137, 3–29.
Aczel, P. and Rathjen, M. (2000/01) Notes on Constructive Set Theory, Institut Mittag-Leffler, Report No. 40.
Aczel, P. and Rathjen, M. (2008) Notes on Constructive Set Theory, available at http://www.mims.manchester.ac.uk/logic/mathlogaps/workshop/CST-book-June-08.pdf, Manchester: Mathlogaps workshop.
Beeson, M.J. (1985) Foundations of Constructive Analysis, Heidelberg: Springer.
Bell, J.L. (1988) Toposes and Local Set Theories; An Introduction, Oxford Logic Guides, Oxford: Clarendon Press.
Acknowledgements
The final stages of writing this paper were carried out at SCAS, the Scandinavian Collegium for Advanced Study, Uppsala University. I am very grateful for the excellent working environment provided by SCAS.
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Aczel, P. (2011). Local Constructive Set Theory and Inductive Definitions. In: Sommaruga, G. (eds) Foundational Theories of Classical and Constructive Mathematics. The Western Ontario Series in Philosophy of Science, vol 76. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0431-2_10
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