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Theories and Ordinals in Proof Theory
Synthese 148 (3):719-743 (2006)
Abstract
How do ordinals measure the strength and computational power of formal theories? This paper is concerned with the connection between ordinal representation systems and theories established in ordinal analyses. It focusses on results which explain the nature of this connection in terms of semantical and computational notions from model theory, set theory, and generalized recursion theoryAuthor's Profile
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Citations of this work
Predicativity and Feferman.Laura Crosilla - 2017 - In Gerhard Jäger & Wilfried Sieg (eds.), Feferman on Foundations: Logic, Mathematics, Philosophy. Cham: Springer. pp. 423-447.
Slow consistency.Sy-David Friedman, Michael Rathjen & Andreas Weiermann - 2013 - Annals of Pure and Applied Logic 164 (3):382-393.
Relativized ordinal analysis: The case of Power Kripke–Platek set theory.Michael Rathjen - 2014 - Annals of Pure and Applied Logic 165 (1):316-339.
Set theory: Constructive and intuitionistic ZF.Laura Crosilla - 2010 - Stanford Encyclopedia of Philosophy.
Fundamental sequences and fast-growing hierarchies for the Bachmann-Howard ordinal.David Fernández-Duque & Andreas Weiermann - 2024 - Annals of Pure and Applied Logic 175 (8):103455.
References found in this work
Admissible sets and structures: an approach to definability theory.Jon Barwise - 1975 - New York: Springer Verlag.
Hilbert's program relativized: Proof-theoretical and foundational reductions.Solomon Feferman - 1988 - Journal of Symbolic Logic 53 (2):364-384.
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