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Uniform Gentzen systems

Published online by Cambridge University Press:  12 March 2014

Raymond M. Smullyan
Raymond M. Smullyan*
Affiliation:
Belfer Graduate School of Science, Yeshiva University
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Extract

Generally speaking, it appears correct to say that in a formulation of first order logic in which a large number of connectives are taken as primitive (e.g. ∼, Λ, ∨, ⊃, ∀, ∃ as opposed to ∼, ⊃, ∀, or still more economically, ↓, ∀ proofs within the formal system tend to be smoother and more natural, but the metatheory tends to be that much more elaborate. In [1] we introduced a unifying ‘α, β, γ, δ” notation (which we also used in [2]–[7] and which we briefly review in this paper) which allows us to have our cake and eat it too.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 33 , Issue 4 , January 1969, pp. 549 - 559
Copyright
Copyright © Association for Symbolic Logic 1969

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References

[1]Smullyan, R. M., A unifying principle in quantification theory, Proceedings of the national academy of sciences, vol. 49 (1963), pp. 828–832.CrossRefGoogle Scholar
[2]Smullyan, R. M., Analytic natural deduction, this Journal, vol. 30 (1965), pp. 123–139.Google Scholar
[3]Smullyan, R. M., Trees and nest structures, this Journal, vol. 31 (1966), pp. 303–321.Google Scholar
[4]Smullyan, R. M., Finite nest structures and prepositional logic, this Journal, vol. 31 (1966), pp. 322–324.Google Scholar
[5]Smullyan, R. M., First order logic, Springer-Verlag, Berlin (to appear).CrossRefGoogle Scholar
[6]Smullyan, R. M., The tableau method In quantification theory, Transactions of the New York Academy of Sciences (to appear).Google Scholar
[7]Smullyan, R. M., Abstract quantification theory, Transactions of the New York Academy of Science (to appear).Google Scholar
[8]Kleene, S. C., Introduction to metamatkematics, Van Nostrana, Princeton, N.J., 1952.Google Scholar
[9]Beth, E. W., The foundations of mathematics, North-Holland, Amsterdam, 1959.Google Scholar
[10]Schütte, K., Beweistheorie, Springer-Verlag, Berlin, 1960.Google Scholar
[11]Kanger, S., Probability In logic, Acta Universitatis Stockholmiensis Stockholm Studies in Philosophy 1, Almquist & Wiksell, Stockholm.Google Scholar
[12]Lyndon, R., Notes on logic. Van Nostrand Mathematical Studies #6, Princeton, N.J.Google Scholar