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 theory | |||||||||
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John E. Hutchinson (1976). Order Types of Ordinals in Models of Set Theory. Journal of Symbolic Logic 41 (2):489-502.
Reinhard Kahle (2002). Mathematical Proof Theory in the Light of Ordinal Analysis. Synthese 133 (1-2):237 - 255.
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Jeremy Avigad & Richard Sommer (1999). The Model-Theoretic Ordinal Analysis of Theories of Predicative Strength. Journal of Symbolic Logic 64 (1):327-349.
Gerhard Jäger & Thomas Strahm (1996). Some Theories with Positive Induction of Ordinal Strength Φω. Journal of Symbolic Logic 61 (3):818-842.
Gerhard Jäger & Barbara Primo (1992). About the Proof-Theoretic Ordinals of Weak Fixed Point Theories. Journal of Symbolic Logic 57 (3):1108-1119.
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