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Abstract

We introduce and investigate a uniform framework for large cardinal operators. This framework accommodates the Ramsey operator, and we show that it also accommodates the subtle operator, the ineffability operator, and the pre-Ramsey operator. We use this framework to introduce several new large cardinal operators, which are closely connected to established large cardinal notions, such as weakly Ramsey and strongly Ramsey cardinals. As a test application for our framework, we show that a strong form of the results of James Baumgartner connecting ineffability to subtlety, and Ramseyness to pre-Ramseyness, generalizes to many further large cardinals and their related operators.