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Remarks on an infinitary language with constructive formulas

Published online by Cambridge University Press:  12 March 2014

E. G. K. Lopez-Escobar
E. G. K. Lopez-Escobar*
Affiliation:
Massachusetts Institute of Technology
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Extract

It is well known that L, the first-order predicate calculus, is unsuitable for characterizing certain mathematical structures. Since some of those structures are quite often considered by mathematicians, extensions of L have been considered which (partially) solve the above problem. Roughly speaking, the extensions of L fall into two main categories:

(I) extensions obtained by allowing higher order variables, and

(II) extensions obtained by allowing infinitely long formulas.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 32 , Issue 3 , 09 October 1967 , pp. 305 - 318
Copyright
Copyright © Association for Symbolic Logic 1967

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References

[F]Feferman, S., Arithmetization of metamathematics in a general setting, Fundamenta mathematieae, vol. 49 (1960), pp. 35–92.CrossRefGoogle Scholar
[K1]Karp, C., Languages with infinitely long expressions. North Holland Publishing Co., Amsterdam, 1964.Google Scholar
[K2]Karp, C., Finite-quantifier equivalence, The theory of models, North Holland Publishing Co., Amsterdam, 1965.Google Scholar
[KL1]Kleene, S. C., On notation for ordinal numbers, this Journal, vol. 3 (1938), pp. 150–155.Google Scholar
[KL2]Kleene, S. C., Introduction to metamathematics, Van Nostrand Publishing Co., Amsterdam, 1952.Google Scholar
[K/T]Kino, A and Takeuti, G., On predicates with infinitely long expressions, Journal of the Mathematical Society of Japan, vol. 15 (1963), pp. 176–190.Google Scholar
[L]Lopez-Escobar, E. G. K., An interpolation theorem for denumerably long formulas, Fundamenta mathematieae, vol. 57 (1965), pp. 253–272.CrossRefGoogle Scholar
[R]Rogers, H. Jr., Theory of recursive functions and effective computability, McGraw-Hill Publishing Co., New York, 1966.Google Scholar
[R/S]Rasiowa, H. and Sikorski, R., On Gentzen theorem, Fundamenta mathematicae, vol. 48 (1960), pp. 57–69.Google Scholar
[S]Scott, D., Logic with denumerably long formulas and finite strings of quantifiers, The theory of models, North Holland Publishing Co., Amsterdam, 1965.Google Scholar
[SH]Shoenfield, J. R., On a restricted ω-rule, Bulletin de l'Academie Polonaise des Sciences, Ser. III, vol. 7 (1959), pp. 405–407.Google Scholar
[T1]Tarski, A., On the concept of truth in formalized languages, Logic, semantics and metamathematics, Oxford University Press, 1956.Google Scholar
[T2]Tarski, A., Remarks on predicate logic with infinitely long expressions, Colloquium mathematicum, vol. 6 (1958), pp. 171–176.CrossRefGoogle Scholar