Operational set theory and small large cardinals
type: Item
instance of: scholarly article
title: Operational set theory and small large cardinals
zbMATH Open document ID: 1183.03044
author: Solomon Feferman
published in: Information and Computation
publication date: 2009-10-09T00:00:00Z
review text: Large cardinals that are consistent with \(V=L\) are called small large cardinals. They appear in various guises in various systems such as admissible set theory, admissible recursion theory, constructive set theory, constructive type theory, etc. The author's grand aim in progress is ``to develop a common language in which such notions can be expressed and can be interpreted both in their original classical form and in their analogue form in each of these special constructive and semi-constructive cases.'' Operational set theory presented in this paper is a partial modification of the author's [Algebra Logic, Papers Summer Res. Inst., Clayton 1974, Lect. Notes Math. 450, 87--139 (1975; Zbl 0357.02029)]. Small large cardinals treated in the paper are inaccessible, Mahlo and weakly compact. A preliminary version of this paper was presented in [Lect. Notes Log. 6, 3--22 (1996; Zbl 0857.03034)].
reviewed by: Hirokazu Nishimura
Mathematics Subject Classification ID: 03E70
Mathematics Subject Classification ID: 03E55
zbMATH DE Number: 5611731
zbMATH Keywords: operational set theory
zbMATH Keywords: small large cardinal notions
zbMATH Keywords: operational closure conditions
MaRDI profile type: Publication
full work available at URL: j.ic.2008.04.007
OpenAlex ID: W1971165519
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DOI: 10.1016/J.IC.2008.04.007
description: scientific article; zbMATH DE number 5611731