Published: 1972 Received: October 26, 1970Available on J-STAGE: September 29, 2006Accepted: -
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Date of correction: September 29, 2006Reason for correction: -Correction: CITATIONDetails: Right : [1] J. Barwise, Infinitary Logic and Admissible Sets, J. Symbolic Logic, 34 (1969), 226-252. [2] J. Barwise, Infinitary Logic and Admissible Sets, Dissertation, Stanford Univ., 1967. [3] J. Denton and B. Dreben, Herbrand-style Consistency Proofs, (Unpublished). [4] S. Feferman, Lectures on Proof Theory, Proc. of the Summer School in Logic, Leeds, 1967, Lecture Notes in Math., No. 70, Springer-Verlag, 1968, pp. 1-107. [5] C. Karp, Languages with Expressions of Infinite Length, North-Holland Publ. Co., Amsterdam, 1964. [6] S. C. Kleene, Mathematical Logic, John Wiley and Sons, Inc., New York, 1967. [7] G. Kreisel, On the Concepts of Completeness and Interpretation of Formal Systems, Fund. Math., 39 (1952), 103-127. [8] G. Kreisel and J. L. Krivine, Elements of Mathematical Logic, North-Holland Publ. Co., Amsterdam, 1967. [9] J. Malitz, Problems in the Model Theory of Infinitary Languages, Doctoral Dissertation, Univ. of California, Berkeley, California, 1965. [10] R. Smullyan, First-order Logic, Springer-Verlag, New York, 1968. [11] W. W. Tait, Normal Derivability in Classical Logic, The Syntax and Semantics of Infinitary Languages, Lecture Notes in Math., No. 72, Springer-Verlag, 1968, pp. 204-236. [12] G. Takeuti, A Determinate Logic, Nagoya Math. J., 38 (1970), 113-138. [13] G. Takeuti, Consistency Proofs of Subsystems of Classical Analysis, Ann. of Math., 86 (1967), 299-348.
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