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A hierarchy of Ramsey cardinals. (English) Zbl 0719.03025

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.

MSC:

03E55 Large cardinals
03E45 Inner models, including constructibility, ordinal definability, and core models
03E05 Other combinatorial set theory
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[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
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