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Ordinal analysis of bar recursion of type zero. (English) Zbl 0444.03030

MSC:
03F10 Functionals in proof theory
03F15 Recursive ordinals and ordinal notations
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References:
[1] H. Gerber : An extension of Schütte’s Klammersymbols . Mathematische Annalen, 174 (1967), 203-216. · Zbl 0162.01901 · doi:10.1007/BF01360719 · eudml:161637
[2] H. Gerber , Brouwer’s bar theorem and a system of ordinal notations . Proceedings of the Summer Conference on Intuitionism and Proof Theory. North-Holland, Amsterdam, 1970. · Zbl 0205.01103
[3] W. Howard , Functional interpretation of bar induction by bar recursion . Compositio Mathematica 20 (1968) 107–124. · Zbl 0162.31503 · numdam:CM_1968__20__107_0 · eudml:88970
[4] W. Howard , A system of abstract ordinals . Journal of Symbolic Logic, 37 (1972) 355-374. · Zbl 0264.02026 · doi:10.2307/2272979
[5] W. Howard , Ordinal analysis of terms of finite type , (to appear). · Zbl 0444.03029 · doi:10.2307/2273417
[6] W. Howard , Ordinal analysis of simple cases of bar recursion , (to appear). · Zbl 0463.03031 · doi:10.2307/2273252
[7] H. Vogel , Über die mit dem Bar-Rekursor vom Type 0 definierbaren Ordinalzahlen . Archiv für Mathematische Logik und Grundlagenforschung 19 (1978) 139-156. · Zbl 0414.03034 · doi:10.1007/BF02011877 · eudml:137954
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