Operational set theory and small large cardinals
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)].
scientific article; zbMATH DE number 5611731
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