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Cut-elimination for impredicative infinitary systems part I. Ordinal-analysis for ID1

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References

  1. Barwise, J.: Admissible sets and structures. Berlin, Heidelberg, New York: Springer 1975.

    Google Scholar 

  2. Bridge, J.: A simplification of the Bachmann method for generating large countable ordinals. J. Symb. Logic40, 171–185 (1975).

    Google Scholar 

  3. Buchholz, W.: Normalfunktionen und konstruktive Systeme von Ordinalzahlen. In: Lecture Notes in Mathematics, Vol. 500, pp. 4–25. Berlin, Heidelberg, New York: Springer 1975.

    Google Scholar 

  4. Buchholz, W.: Über Teilsysteme von\(\bar \theta \){g}. Arch. Math. Logik18, 85–98 (1976).

    Google Scholar 

  5. Buchholz, W.: Ordinal analysis of IDc andW-IDc. Preliminary version. Munich (1977) Mimeographed.

  6. Buchholz, W.: Eine Erweiterung der Schnitteliminationsmethode. Habilitationsschrift, München 1977.

    Google Scholar 

  7. Buchholz, W., Pohlers, W.: Provable wellorderings of formal theories for transfinitely iterated inductive definitions. J. Symb. Logic43, 118–125 (1978).

    Google Scholar 

  8. Feferman, S.: Systems of predicative analysis. J. Symb. Logic29, 1–30 (1964).

    Google Scholar 

  9. Feferman, S.: Formal theories for transfinite iterations of generalized inductive definitions and some subsystems of analysis. Intuitionism and proof theory, pp. 303–326. Amsterdam: North-Holland 1970.

    Google Scholar 

  10. Gerber, H.: Brouwer's bar theorem and a system of ordinal notation. Intuitionism and proof theory, pp. 327–338. Amsterdam: North-Holland 1970.

    Google Scholar 

  11. Howard, W.: Assignment of ordinals to terms for type 0 bar recursive functionals (abstract). J. Symb. Logic35, 354 (1970).

    Google Scholar 

  12. Howard, W.: A system of abstract constructive ordinals. J. Symb. Logic37, 355–374 (1972).

    Google Scholar 

  13. Jäger, G.: Beweistheorie von-KPN (to appear in Arch. Math. Logik).

  14. Jäger, G.: Dissertation München 1979.

  15. Kreisel, G.: Generalised inductive definitions. Stanford Report (1963). Mimeographed.

  16. Pohlers, W.: An upper bound for the provability of transfinite induction in systems withn-times iterated inductive definitions. In: Lecture Notes in Mathematics, Vol. 500, pp. 271–289. Berlin, Heidelberg, New York: Springer 1975.

    Google Scholar 

  17. Pohlers, W.: Eine kanonische Interpretation von ID c1 . Lecture at Münster (1976). Mimeographed.

  18. Pohlers, W.: Ordinals connected with formal theories for transfinitely iterated inductive definitions. J. Symb. Logic43, 161–182 (1978).

    Google Scholar 

  19. Pohlers, W.: Beweistheorie der iterierten induktiven Definitionen. Habilitationsschrift, München 1977.

    Google Scholar 

  20. Schütte, K.: Proof theory. Berlin, Heidelberg, New York: Springer 1977.

    Google Scholar 

  21. Sieg, W.: Trees in metamathematics. Thesis Stanford (1977).

  22. Tait, W.: Normal derivability in classical logic. The syntax and semantics of infinitary languages. In: Lecture Notes in Mathematics, Vol. 72, pp. 204–256. Berlin, Heidelberg, New York: Springer 1968.

    Google Scholar 

  23. Tait, W.: Applications of the cut-elimination theorem to some subsystems of classical analysis. Intuitionism and proof theory, pp. 475–488. Amsterdam: North-Holland 1970.

    Google Scholar 

  24. Takeuti, G.: Consistency proofs of subsystems of classical analysis. Ann. Math.86, 299–348 (1967).

    Google Scholar 

  25. Zucker, I.: Iterated inductive definitions, trees and ordinals. Metamathematical investigation of intuitionistic arithmetic and analysis. In: Lecture Notes in Mathematics, Vol. 344, pp. 392–452. Berlin, Heidelberg, New York: Springer 1973.

    Google Scholar 

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Pohlers, W. Cut-elimination for impredicative infinitary systems part I. Ordinal-analysis for ID1 . Arch math Logik 21, 113–129 (1981). https://doi.org/10.1007/BF02011638

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