A theorem on the second-order arithmetic with the ω-rule*)

Motoo TAKAHASHI

doi:10.2969/jmsj/02210015

A theorem on the second-order arithmetic with the ω-rule_*)

Motoo TAKAHASHI

Author information

JOURNAL FREE ACCESS

1970 Volume 22 Issue 1 Pages 15-24

DOI https://doi.org/10.2969/jmsj/02210015

Details

Published: 1970 Received: December 03, 1968 Available on J-STAGE: September 29, 2006 Accepted: - Advance online publication: - Revised: -
Correction information
Date of correction: September 29, 2006 Reason for correction: - Correction: TITLE Details: Wrong : A theorem on the second-order arithmetic with the ω-rule
Right : A theorem on the second-order arithmetic with the ω-rule_*)

Date of correction: September 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) A. Grzegorczyk, A. Mostowski and C. Rull-Nardzewski, The Classical and the ω-complete arithmetic, J. Symbolic Logic, 23 (1958), 188-206.
2) S.C. Kleene, Introduction to metamathematics, New York, Amsterdam and Groningen (1952).
3) J.R. Shoenfield, On a restricted ω-rule, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 7 (1959), 405-407.
4) H. Tanaka, On the HA-restricted ω-rule, mimeographed.
5) E.G.K. Lopez-Escobar, A complete, infinitary axiomatization of weak second-order logic, Fund. Math., 61 (1967), 93-103.
6) E.G.K. Lopez-Escobar, Remarks on an infinitary language with constructive formulas, J. Symbolic Logic, 32 (1967), 305-318.

Right : [1] A. Grzegorczyk, A. Mostowski and C. Rull-Nardzewski, The Classical and the ω-complete arithmetic, J. Symbolic Logic, 23 (1958), 188-206.
[2] S. C. Kleene, Introduction to metamathematics, New York, Amsterdam and Groningen (1952).
[3] J. R. Shoenfield, On a restricted ω-rule, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 7 (1959), 405-407.
[4] H. Tanaka, On the HA-restricted ω-rule, mimeographed.
[5] E. G. K. Lopez-Escobar, A complete, infinitary axiomatization of weak second-order logic, Fund. Math., 61 (1967), 93-103.
[6] E. G. K. Lopez-Escobar, Remarks on an infinitary language with constructive formulas, J. Symbolic Logic, 32 (1967), 305-318.

Date of correction: September 29, 2006 Reason for correction: - Correction: PDF FILE Details: -

Corresponding author

Correction information

Register with J-STAGE for free!