By A.I. Arruda, et al

ISBN-10: 0444854029

ISBN-13: 9780444854025

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CuU Journal of Formal Logic IX, 1978. New York. > , Notre Dame pp. 359-366. * A plto06--theolLeUc. > C"" in Mathematical Logic: Proceedings of the First Brazilian Conference (Eds. A. I. Arru- da, N. C. A. da Costa and R. Chuaqui), Marcel Dekker, New York, 233-240. pp. L. S. Rogowski. 1964. Log-ika. k-ieltunkowa. >pILeQznoiQi zmiany (V-ilLemonal. o on the. mon 06 dumgeJ, Studia Societatis Scientiarum Torunensis XV, pp. 5-92. J. B. Rosser. *1953. Logic for Mathematicians, McGraw-Hi 11, New York. R.

1975. i, Studia Logica XXXIV, pp. 149-168. J. Kotas and N. C. A. da Costa. 1977. i'h (Ed. A. I. Arruda, N. C. A. da Costa and R. Chuaqui), North-Holland, Amsterdam, pp. 57-73. and Computability 1978. On the. i and the. icz, 36 AYDA I. ARRUDA in Mathematical Logic: Proceedings of the First Brazilian Conference (Eds. A. 1. Arruda, N. C. A. da Costa Marcel Dekker, New York, and R. Chuaqui), pp. 127-139. 197+a. on 06 cU6cJL6f>ive logie, 197+b. PfWblvrJ,6 on moda£. and cU6ruMive logie, to appear. to appear.

U>ey then IIRII = N. Clearly, this is a schema; note that even though m does not appear in the scope of the quantifier one should remember that R stands for a formul a which may have m as a variable besides, of course, some other variables which are quantified over universally. 5. hema (Aolt. valent: PA. For convenience we write the induction schema a follows: \;/x (\;/y (If C x ~ ¢(y))~ ¢(x))~ \;/x ¢(x) This is easily seen to be equivalent to the usual induction schema axiom of foundation in this set-up).

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