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A simplified ordinal analysis of first-order reflection. (English) Zbl 1485.03234

Summary: In this note we give a simplified ordinal analysis of first-order reflection. An ordinal notation system \(OT\) is introduced based on \(\psi\)-functions. Provable \(\Sigma_1\)-sentences on \(L_{\omega_1^{CK}}\) are bounded through cut-elimination on operator controlled derivations.

MSC:

03F15 Recursive ordinals and ordinal notations
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