On provably recursive functions and ordinal recursive functions
ジャーナル
フリー
1968 年 20 巻 3 号 p. 456-476
詳細
- Published: 1968 Received: 1966/10/24 Available on J-STAGE: 2006/09/26 Accepted: - Advance online publication: - Revised: -
-
訂正情報
訂正日: 2006/09/26 訂正理由: - 訂正箇所: 引用文献情報 訂正内容: Wrong : 1) G. Gentzen, Untersuchungen über das logische Schliessen, I, II, Math. Z., 39 (1934), 176-210, 405-431.
2) G. Gentzen, Neue Fassung des Widerspruchsfreiheitsbeweis für die reine Zahlentheorie. Forschungen zur Logik and zur Grundlegung der exakten Wissenschaften, Neue Folge 4, Leipzig, 1938, 19-44.
3) G. Gentzen, Beweisbarkeit und Unbeweisbarkeit von Anfangsfällen der transfiniten Induktion in der reinen Zahlentheorie, Mathematishe Annalen, 119 (1943), 140-161.
4) K. Gödel, Über eine bisher noch benutzte Erweiterung des finiten Standpunktes, Dialectica, 12 (1958), 280-287.
5) S. C. Kleene, Introduction to Metamathematics, North-Holland, New York, Amsterdam and Groningen, 1952.
6) G. Kreisel, On the, interpretation of non-finitist proofs, J. Symb. Logic, 16 (1951), 241-267, and 17 (1952), 43-58, See Erratum, J. Symb. Logic, 17, iv.
7) G. Kreisel, Interpretation of analysis by means of constructive functionals of finite types, Constructivity in Mathematics, Amsterdam, 1959, 101-128.
8a) G. Kreisel, Proof by transfinite induction and definition by transfinite induction in quantifier-free systems, (abstract), J. Symb. Logic, 24 (1959), 322-323.
8b) G. Kreisel, Inessential extensions of Heyting's arithmetic by means of functionals of finite types, (abstract), J. Symb. Logic, 24 (1959), 284.
8c) G. Kreisel, Status of the first ε-number in first order arithmetic, (abstract), J. Symb. Logic, 25 (1960), 390.
9) G. Kreisel, Mathematical Logic, Lectures on Modern Mathematics, 3, New York, 1965, 95-195.
10) W. W. Tait, A characterization of ordinal recursive functions, (abstract), J. Symb. Logic, 24 (1959), 325.
11) G. Takeuti, On a generalized logic calculus, Japan. J. Math., 23 (1953), 39-96.Errata to “On a generalized logic calculus”, Japan. J. Math., 24 (1954), 149-156.
12) G. Takeuti, On the fundamental conjecture of GLC, I, J. Math. Soc. Japan, 7 (1955), 249-275.
13) G. Takeuti, On the fundamental conjecture of GLC, III, J. Math. Soc. Japan, 8 (1956), 54-64.
14) G. Takeuti, Ordinal diagrams, J. Math. Soc. Japan, 9 (1957), 386-394.
15) G. Takeuti, On the fundamental conjecture of GLC, V, J. Math. Soc. Japan, 10 (1958), 121-134.
16) G. Takeuti, On the formal theory of ordinal diagrams, Ann. Japan Assoc. Philos. Sci., 3 (1958), 151-170.
17) G. Takeuti, Ordinal diagrams, II, J. Math. Soc. Japan, 12 (1960), 385-391.
18) G. Takeuti, On the fundamental conjecture of GLC, VI, Proc. Japan Acad., 37 (1961), 437-439.
19) G. Takeuti, On the inductive definition with quantifiers of second order, J. Math. Soc. Japan, 13 (1961), 333-341.
20) G. Takeuti, A remark on Gentzen's paper “Beweisbarkeit and Unbeweisbarkeit von Anfangsfällen der transfiniten Induktion in der reinen Zahlentheorie”, I, II, Proc. Japan Acad., 39 (1963), 263-269.
21) G. Takeuti, Consistency proofs of subsystems of classical analysis, Ann. of Math., 86 (1967), 299-348.
Right : [1] G. Gentzen, Untersuchungen über das logische Schliessen, I, II, Math. Z., 39 (1934), 176-210, 405-431.
[2] G. Gentzen, Neue Fassung des Widerspruchsfreiheitsbeweis für die reine Zahlentheorie, Forschungen zur Logik und zur Grundlegung der exakten Wissenschaften, Neue Folge 4, Leipzig, 1938, 19-44.
[3] G. Gentzen, Beweisbarkeit und Unbeweisbarkeit von Anfangsfällen der transfiniten Induktion in der reinen Zahlentheorie, Mathematishe Annalen, 119 (1943), 140-161.
[4] K. Gödel, Über eine bisher noch benutzte Erweiterung des finiten Standpunktes, Dialectica, 12 (1958), 280-287.
[5] S. C. Kleene, Introduction to Metamathematics, North-Holland, New York, Amsterdam and Groningen, 1952.
[6] G. Kreisel, On the interpretation of non-finitist proofs, J. Symb. Logic, 16 (1951), 241-267, and 17 (1952), 43-58, See Erratum. J. Symb. Logic, 17, iv.
[7] G. Kreisel, Interpretation of analysis by means of constructive functionals of finite types, Constructivity in Mathematics, Amsterdam, 1959, 101-128.
[8a] G. Kreisel, Proof by transfinite induction and definition by transfinite induction in quantifier-free systems, (abstract), J. Symb. Logic, 24 (1959), 322-323.
[8b] G. Kreisel, Inessential extensions of Heyting's arithmetic by means of functionals of finite types, (abstract), J. Symb. Logic, 24 (1959), 284.
[8c] G. Kreisel, Status of the first ε-number in first order arithmetic, (abstract), J. Symb. Logic, 25 (1960), 390.
[9] G. Kreisel, Mathematical Logic, Lectures on Modern Mathematics, 3, New York, 1965, 95-195.
[10] W. W. Tait, A characterization of ordinal recursive functions, (abstract), J. Symb. Logic, 24 (1959), 325.
[11] G. Takeuti, On a generalized logic calculus, Japan. J. Math., 23 (1953), 39-96. Errata to “On a generalized logic calculus”, Japan. J. Math., 24 (1954), 149-156.
[12] G. Takeuti, On the fundamental conjecture of GLC, I, J. Math. Soc. Japan, 7 (1955), 249-275.
[13] G. Takeuti, On the fundamental conjecture of GLC, III, J. Math. Soc. Japan, 8 (1956), 54-64.
[14] G. Takeuti, Ordinal diagrams, J. Math. Soc. Japan, 9 (1957), 386-394.
[15] G. Takeuti, On the fundamental conjecture of GLC, V, J. Math. Soc. Japan, 10 (1958), 121-134.
[16] G. Takeuti, On the formal theory of ordinal diagrams, Ann. Japan Assoc. Philos. Sci., 3 (1958), 151-170.
[17] G. Takeuti, Ordinal diagrams, II, J. Math. Soc. Japan, 12 (1960), 385-391.
[18] G. Takeuti, On the fundamental conjecture of GLC, VI, Proc. Japan Acad., 37 (1961), 437-439.
[19] G. Takeuti, On the inductive definition with quantifiers of second order, J. Math. Soc. Japan, 13 (1961), 333-341.
[20] G. Takeuti, A remark on Gentzen's paper “Beweisbarkeit und Unbeweisbarkeit von Anfangsfällen der transfiniten Induktion in der reinen Zahlentheorie”, I, II, Proc. Japan Acad., 39 (1963), 263-269.
[21] G. Takeuti, Consistency proofs of subsystems of classical analysis, Ann. of Math., 86 (1967), 299-348.
訂正日: 2006/09/26 訂正理由: - 訂正箇所: PDFファイル 訂正内容: -
PDFをダウンロード (1848K)
メタデータをダウンロード
RIS形式
BIB TEX形式
テキスト
メタデータのダウンロード方法
発行機関連絡先
(EndNote、Reference Manager、ProCite、RefWorksとの互換性あり)
(BibDesk、LaTeXとの互換性あり)
記事の1ページ目
