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Beweistheoretische Abgrenzung von Teilsystemen der Analysis. (German) Zbl 0434.03040

MSC:

03F35 Second- and higher-order arithmetic and fragments
03F15 Recursive ordinals and ordinal notations
03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations
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References:

[1] Buchholz, W.: Über Teilsysteme von \(\bar \theta (\{ g\} )\) . Arch. f. Math. Logik u. Grundl.18, 85–98 (1976). · Zbl 0366.02017 · doi:10.1007/BF02007261
[2] Buchholz, W., undW. Pohlers: Provable wellorderings of formal theories for transfinitely iterated inductive definitions. J. Symb. Logic43, 118–125 (1978). · Zbl 0411.03046 · doi:10.2307/2271954
[3] Buchholz, W., undK. Schütte: Syntaktische Abgrenzungen von formalen Systemen der \(\prod _1^1\) -Analysis und \(\Delta _2^1\) -Analysis. Sitzber. Bayer. Akad. d. Wiss. Math.-Nat. Kl. 1980.
[4] Feferman, S.: Systems of predicative analysis. J. Symb. Logic29, 1–30 (1964). · Zbl 0134.01101 · doi:10.2307/2269764
[5] Feferman, S.: Formal theories of transfinite iterations of generalized inductive definitions and some subsystems of analysis. Intuitionism and Proof Theory, pp. 303–326. Amsterdam: North-Holland. 1970. · Zbl 0218.02024
[6] Friedman, H.: Iterated inductive definitions and \(\sum _2^1\) -AC. Intuitionism and Proof Theory, pp. 435–442. Amsterdam: North-Holland. 1970.
[7] Gentzen, G.: Neue Fassung des Widerspruchsfreiheitsbeweises für die reine Zahlentheorie. Forsch. Logik u. Grundlegung d. exakten Wiss. n. s.4, 19–44 (1938). · JFM 64.0027.03
[8] Gentzen, G.: Beweisbarkeit und Unbeweisbarkeit von Anfangsfällen der transfiniten Induktion in der reinen Zahlentheorie. Math. Ann.119, 149–161 (1943). · Zbl 0028.10201 · doi:10.1007/BF01564760
[9] Gödel, K.: Über formal unentscheidbare Sätze der Principia mathematica und verwandter Systeme, I. Mh. Math. Phys.38, 173–198 (1931). · JFM 57.0054.02
[10] Gödel, K.: The Consistency of the Axiom of Choice and of the Generalized Continuum-hypothesis with the Axioms of Set Theory. Ann. Math. Studies, no. 3. Princeton, N. J. 1940.
[11] Gödel, K.: Über eine bisher noch nicht benützte Erweiterung des finiten Standpunktes. Dialectica12, 280–287 (1958). · Zbl 0090.01003 · doi:10.1111/j.1746-8361.1958.tb01464.x
[12] Jäger, G.: Die konstruktible Hierarchie als Hilfsmittel zur beweistheoretischen Untersuchung von Teilsystemen der Mengenlehre und Analysis. Dissertation. München 1979. · Zbl 0449.03057
[13] Pohlers, W.: Ordinals connected with formal theories for transfinitely iterated inductive definitions. J. Symb. Logic43, 161–182 (1978). · Zbl 0394.03049 · doi:10.2307/2272816
[14] Schütte, K.: Proof Theory. Berlin-Heidelberg-New York: Springer. 1977. · Zbl 0367.02012
[15] Spector, C.: Provably recursive functionals of analysis: a consistency proof of analysis by an extension of principles formulated in current intuitionistic mathematics. Symp. Pure Math. Amer. Math. Soc.5, 1–27 (1962). · Zbl 0143.25502
[16] Takeuti, G.: Consistency proofs of subsystems of classical analysis. Ann. Math.86, 299–348 (1967). · Zbl 0159.00905 · doi:10.2307/1970691
[17] Zucker, J.: Iterated inductive definitions, trees and ordinals. Springer Lecture Notes Math. 344, p. 392–453. Berlin-Heidelberg-New York: Springer. 1973.
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