Feng, Qi A hierarchy of Ramsey cardinals. (English) Zbl 0719.03025 Ann. Pure Appl. Logic 49, No. 3, 257-277 (1990). Hierarchies of large cardinal properties between Ramsey and measurable are introduced and studied. The properties, somewhat similar to iterated Mahloness, but using the Ramsey filter rather than the club filter, are absolute to the core model. Reviewer: P.Komjáth (Budapest) Cited in 8 Documents MSC: 03E55 Large cardinals 03E45 Inner models, including constructibility, ordinal definability, and core models 03E05 Other combinatorial set theory Keywords:Ramsey cardinals; ideals; absoluteness; measurable cardinals; Hierarchies of large cardinal properties; core model PDF BibTeX XML Cite \textit{Q. Feng}, Ann. Pure Appl. Logic 49, No. 3, 257--277 (1990; Zbl 0719.03025) Full Text: DOI OpenURL References: [1] Baumgartner, J., Ineffability properties of cardinals I, (), 109-130 · Zbl 0313.04002 [2] Baumgartner, J., Ineffability properties of cardinals II, (), 87-106, Reidel, Dordrecht · Zbl 0373.04002 [3] Dodd, T., The core model, London math. soc. lecture note series, 61, (1982), Cambridge Univ. Press Cambridge · Zbl 0474.03027 [4] Dodd, T.; Jensen, R., The core model, Ann. math. logic, 20, 43-75, (1981) · Zbl 0457.03051 [5] Donder, D.; Jensen, R.; Koppelberg, B., Some applications of the core model, (), 55-97 [6] Erdös, P.; Rado, R., A partition calculus in set theory, Bull. amer. math. soc., 62, 427-489, (1956) · Zbl 0071.05105 [7] Fodor, G., Eine bemerkung zur theorie der regressiven funktionen, Acta sci. math., 17, 139-142, (1956), (Szeged) · Zbl 0072.04302 [8] Jech, T., Set theory, (1978), Academic Press New York · Zbl 0419.03028 [9] Jech, T., Stationary subsets of inaccessible cardinals, (), 115-142 · Zbl 0555.03024 [10] Jech, T.; Prikry, K., Ideals over uncountable sets: application of almost disjoint functions and generic ultrapowers, Mem. amer. math. soc., 214, (1979) · Zbl 0398.03044 [11] Levy, A., The sizes of indescribable cardinals, (), 205-218, Part 1 [12] Mitchell, W., Ramsey cardinals and constructibility, J. symbolic logic, 44, 260-266, (1979) · Zbl 0409.03033 [13] Ramsey, F., On a problem of formal logic, Proc. London math. soc., 30, 2, 264-286, (1930) · JFM 55.0032.04 [14] Rowbottom, F., Large cardinals and constructible sets, Doctoral dissertation, (1964), University of Wisconsin Madison, WI [15] Scott, D., Measurable cardinals and constructible sets, Bull. acad. polon. sci., ser. sci. math. astronom. phys., 7, 145-149, (1961) · Zbl 0154.00702 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.