Model theory on a positive second order logic with countable conjunctions and disjunctions

Nobuyoshi MOTOHASHI

doi:10.2969/jmsj/02510027

Nobuyoshi MOTOHASHI

著者情報

ジャーナルフリー

1973 年 25 巻 1 号 p. 27-42

DOI https://doi.org/10.2969/jmsj/02510027

詳細

Published: 1973 Received: 1971/11/09 Available on J-STAGE: 2006/09/29 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/09/29 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) J. Barwise, Remark on universal sentences of L_ω₁ω, Duke Math. J., 36 (1969),631-637.
2) C. C. Chang, On unions of chains of models, Proc. Amer. Math. Soc., 10 (1959), 120-127.
3) C. C. Chang, Some remarks on the model theory of infinitary languages, in “the Syntax and Semantics of Infinitary languages” edited by J. Barwise, Lecture Notes in Math. No. 72, Springer-Verlag, 1968, 36-63.
4) S. Feferman and G. Kreisel, Persistent and invariant formulas relative to theories of higher order, Bull. Amer. Math. Soc., 72 (1966), 480-485.
5) H. J. Keisler, Unions of relational systems, Proc. Amer. Math. Soc., 15 (1964), 540-545.
6) H J. Keisler, Some applications of infinitely long formulas, J. Symbolic Logic, 30 (1965), 339-349.
7) H. J. Keisler, Model theory for infinitary logic, North Holland, 1971.
8) N. Motohashi, Interpolation theorem and characterization theorem, Ann. Japan Assoc. Philos. Sci., 4 (1972), 85-150.
9) M. Makkai, On the model theory of denumerably long formulas with finite strings of quantifiers, J. Symbolic Logic, 34 (1969), 437-459.
10) J. Malitz, Universal classes in infinitary languages, Duke. Math. J., 36 (1969), 621-630.
11) G. E. Reyes, Local definability theory, Ann. of Math., Logic, 1 (1970), 95-137.
12) R. C. Lyndon, Properties preserved under homomorphism, Pacific J. Math., 9 (1959), 143-154.
13) J. Los, On the extending of models, I, Fund. Math., 42 (1955), 38-54.
14) E. G. K. Lopez-Escobar, An interpolation theorem for denumerably long formulas, Fund. Math., 57 (1965), 253-272.
15) D. Scott, Logic with denumerably long formulas and finite strings of quantifiers, in Theory of Models, North-Holland, 1965, 329-341.
16) A. Tarski, Contributions to the theory of models, Indag, Math., 16 (1954), Part I 572-581, Part II 582-588; 17 (1955), Part III 56-64.
17) S. Maehara and G. Takeuti, Two interpolation theorems for a Π₁¹ predicate calculus, J. Symbolic Logic, 36 (1971), 262-270.
18) R. Vaught, The Löwenheim-Skolem theorem, in Proc. of the 1964 Int'l Cong. Logic Math. and Phil. Sci. held in Jerusalem, 81-89.
19) J. Weinstein, (ω₁, ω)-properties of unions of models, in “the Syntax and Semanticsof Infinitary Languages”, edited by J. Barwise, Lecture Note in Math., No. 72, Springer-Verlag, 1968, 265-268.
20) N. Motohashi, Object logic and morphism logic, J. Math. Soc. Japan, 24 (1972), 684-697.
21) M. Takahashi, Δ₁-definability in set theory, in “Conference in Mathematical Logic, London '70”, Lecture Note in Math., No. 255, Springer-Verlag, 1972, 281-304.

Right : [1] J. Barwise, Remark on universal sentences of L_ω₁ω, Duke Math. J., 36 (1969), 631-637.
[2] C. C. Chang, On unions of chains of models, Proc. Amer. Math. Soc., 10 (1959), 120-127.
[3] C. C. Chang, Some remarks on the model theory of infinitary languages, in “the Syntax and Semantics of Infinitary languages” edited by J. Barwise, Lecture Notes in Math. No. 72, Springer-Verlag, 1968, 36-63.
[4] S. Feferman and G. Kreisel, Persistent and invariant formulas relative to theories of higher order, Bull. Amer. Math. Soc., 72 (1966), 480-485.
[5] H. J. Keisler, Unions of relational systems, Proc. Amer. Math. Soc., 15 (1964), 540-545.
[6] H. J. Keisler, Some applications of infinitely long formulas, J. Symbolic Logic, 30 (1965), 339-349.
[7] H. J. Keisler, Model theory for infinitary logic, North Holland, 1971.
[8] N. Motohashi, Interpolation theorem and characterization theorem, Ann. Japan Assoc. Philos. Sci., 4 (1972), 85-150.
[9] M. Makkai, On the model theory of denumerably long formulas with finite strings of quantifiers, J. Symbolic Logic, 34 (1969), 437-459.
[10] J. Malitz, Universal classes in infinitary languages, Duke. Math. J., 36 (1969), 621-630.
[11] G. E. Reyes, Local definability theory, Ann. of Math., Logic, 1 (1970), 95-137.
[12] R. C. Lyndon, Properties preserved under homomorphism, Pacific J. Math., 9 (1959), 143-154.
[13] J. Los, On the extending of models, I, Fund. Math., 42 (1955), 38-54.
[14] E. G. K. Lopez-Escobar, An interpolation theorem for denumerably long formulas, Fund. Math., 57 (1965), 253-272.
[15] D. Scott, Logic with denumerably long formulas and finite strings of quantifiers, in Theory of Models, North-Holland, 1965, 329-341.
[16] A. Tarski, Contributions to the theory of models, Indag, Math., 16 (1954), Part I 572-581, Part II 582-588; 17 (1955), Part III 56-64.
[17] S. Maehara and G. Takeuti, Two interpolation theorems for a π₁¹ predicate calculus, J. Symbolic Logic, 36 (1971), 262-270.
[18] R. Vaught, The Löwenheim-Skolem theorem, in Proc. of the 1964 Int'l Cong. Logic Math. and Phil. Sci. held in Jerusalem, 81-89.
[19] J. Weinstein, (ω₁, ω)-properties of unions of models, in “the Syntax and Semantics of Infinitary Languages”, edited by J. Barwise, Lecture Note in Math., No. 72, Springer-Verlag, 1968, 265-268.
[20] N. Motohashi, Object logic and morphism logic, J. Math. Soc. Japan, 24 (1972), 684-697.
[21] M. Takahashi, Δ₁-definability in set theory, in “Conference in Mathematical Logic, London '70”, Lecture Note in Math., No. 255, Springer-Verlag, 1972, 281-304.

訂正日: 2006/09/29 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

責任著者(Corresponding author)

訂正情報

J-STAGEへの登録はこちら（無料）