Abstract
We study the definably-Mahlo, definably-weakly-compact, and the definably-indescribable cardinals, which are the definable versions of, respectively, Mahlo, weakly-compact, and indescribable cardinals. We study their strength as large cardinals and we show that the relationship between them is almost the same as the relationship between Mahlo, weakly-compact and indescribable cardinals.
This paper was partially written during a research stay of the author at the Centre de Recerca Matemàtica (CRM), at the Universitat Autònoma de Barcelona. The author was partially supported by the research projects: BFM2002-03236 of the Spanish Ministry of Science and Technology, PR-01-GE-10-HUM of the Government of the Principado de Asturias, and 2002GR-00126 of the Generalitat de Catalunya.
To Ramon Bastardes, in memoriam
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Bosch, R. (2006). Small Definably-large Cardinals. In: Bagaria, J., Todorcevic, S. (eds) Set Theory. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7692-9_3
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DOI: https://doi.org/10.1007/3-7643-7692-9_3
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