Summary
It is shown how the strong ordinal notation systems that figure in proof theory and have been previously defined by employing large cardinals, can be developed directly on the basis of their recursively large counterparts. Thereby we provide a completely new approach to well-ordering proofs as will be exemplified by determining the proof-theoretic ordinal of the systemKPM of [R91].
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The author would like to thank the National Science Foundation for partially supporting this research by grant DMS-9203443
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Rathjen, M. Collapsing functions based on recursively large ordinals: A well-ordering proof for KPM. Arch Math Logic 33, 35–55 (1994). https://doi.org/10.1007/BF01275469
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DOI: https://doi.org/10.1007/BF01275469