Extending Ideas of Tait for Incorporating Higher-order Parameters in Schemes of Reflection.

We formulate a new reflection principle which subsumes all of the reflection principles which were considered by Tait and Koellner and are also known to be consistent, and which is itself consistent relative to an ω-Erdős cardinal (because equivalent to the existence of a remarkable cardinal). The author was supported by the research grant DE 436/10-1 from Deutsche Forschungsgemeinschaft, while working at the University of Tübingen. Ralf Schindler provided very helpful assistance with identifying errors in earlier versions of the paper and providing a useful characterisation of remarkable cardinals which greatly simplified the argument that a cardinal is extremely reflective if and only if it is remarkable.

Authors

• Rupert McCallum

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