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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.

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
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