Markov's principle and Markov's rule for theores of choice sequences

  • A. S. Troelstra
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 500)


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  1. [D] D. van Dalen, Lectures on intuitionism, in: A. R. D. Mathias, H. Rogers (editors), Cambridge Summer School in Mathematical Logic. Berlin (Springer-Verlag) 1973, pp. 1–94.CrossRefGoogle Scholar
  2. [H] W. A. Howard, A system of abstract constructive ordinals. J. S. L. 37 (1972), pp. 355–374.MathSciNetzbMATHGoogle Scholar
  3. [J] D. H. J. de Jongh, Formulas of one propositional variable in intuitionistic arithmetic. Report 73-03 of the Dept of Mathematics, University of Amsterdam.Google Scholar
  4. [K] S. C. Kleene, Formalized recursive functionals and formalized realizability. Memoirs of the American Math. Soc. nr 89. Providence, Rh. I. 1969.Google Scholar
  5. [Kr1] G. Kreisel, On weak completeness of intuitionistic predicate logic. J. S. L. 27 (1962), pp. 139–158.MathSciNetzbMATHGoogle Scholar
  6. [Kr2]-, Church's thesis: A kind of reducibility axiom for constructive mathematics, in: A. Kino, J. Myhill, R. E. Vesley (editors). Intuitionism and Proof Theory, Amsterdam (North-Holland) 1970, pp. 121–150.Google Scholar
  7. [Kr3] G. Kreisel, A survey of proof theory II, in: J. E. Fenstad (editor), Proceedings of the Second Scandinavian Logic Symposium, Amsterdam (North-Holland) 1971, pp. 109–170.CrossRefGoogle Scholar
  8. [Kr4] G. Kreisel, Theory of free choice sequences of natural numbers, in: Stanford report on the foundations of analysis, Stanford 1963 (mimeographed, privately circulated only), section IV.Google Scholar
  9. [K,T] G. Kreisel and A. S. Troelstra, Formal systems for some branches of intuitionistic analysis. Annals of Mathematical Logic 1 (1970), pp. 229–387.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [K,V] S. C. Kleene and R. E. Vesley, Foundations, of intuitionistic mathematics, especially in relation to recursive functions, Amsterdam (North-Holland) 1965.zbMATHGoogle Scholar
  11. [L] H. Luckhardt, Extensional Gödel functional interpretation. A consistency proof of classical analysis. Springer Lecture Notes Vol. 306, Berlin (Springer) 1973.CrossRefzbMATHGoogle Scholar
  12. [S] H. Schwichtenberg, Einige Anwendungen von unendlichen Termen und Wertfunktionalen. Habilitationsschrift, Münster (Westf.) 1973.Google Scholar
  13. [T1] A. S. Troelstra, Notes on the intuitionistic theory of sequences I, Indag. Math. 31 (1969), pp. 430–440.MathSciNetzbMATHGoogle Scholar
  14. [T2]-, Notes on the intuitionistic theory of sequences III, Indag. Math. 32 (1970), pp. 245–252.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [T3]—, An addendum. Annals of Mathematical Logic 4 (1971), pp. 437–439.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [T4] A. S. Troelstra, Note on the fan theorem. J. S. L. To appear.Google Scholar
  17. [T5]-(editor), Metamathematical Investigation of Intuitionistic Arithmetic and Analysis. Springer Lecture Notes Vol. 344, Berlin (Springer Verlag) 1973.zbMATHGoogle Scholar

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© Springer-Verlag 1975

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  • A. S. Troelstra

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