On the Constructive Dedekind Reals: Extended Abstract
In: Logical Foundations of Computer Science ISBN: 9783540727323 LFCS; (2007-06-28)
Online
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Zugriff:
In order to built the collection of Cauchy reals as a set in constructive set theory, the only Power Set-like principle needed is Exponentiation. In contrast, the proof that the Dedekind reals form a set has seemed to require more than that. The main purpose here is to show that Exponentiation alone does not suffice for the latter, by furnishing a Kripke model of constructive set theory, CZF with Subset Collection replaced by Exponentiation, in which the Cauchy reals form a set while the Dedekind reals constitute a proper class.
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On the Constructive Dedekind Reals: Extended Abstract
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| Autor/in / Beteiligte Person: | Lubarsky, Robert S. ; Rathjen, Michael |
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| Quelle: | Logical Foundations of Computer Science ISBN: 9783540727323 LFCS; (2007-06-28) |
| Veröffentlichung: | Springer Berlin Heidelberg, 2007 |
| Medientyp: | unknown |
| ISBN: | 978-3-540-72732-3 (print) |
| DOI: | 10.1007/978-3-540-72734-7_25 |
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