Recursive \(\omega\)-rule for proof systems. (English) Zbl 0671.03019
By using the result of E. G. K. Lopez-Escobar [Stud. Logic Found. Math. 89, 75–97 (1977; Zbl 0386.03026)] that if there is an effective disjunctor on a formal Carnap theory \({\mathcal F}\), then \({\mathcal F}^{\infty}\) is a conservative extension of \({\mathcal F}^{\infty}_{rec}\), this author shows that infinitary rules in most proof systems in computer science can be restricted to recursive ones.
Reviewer: Hirokazu Nishimura (Tsukuba)
Keywords:
recursive proof systems; effective disjunctor; Carnap theory; infinitary rules; proof systems in computer scienceCitations:
Zbl 0386.03026References:
| [1] | Lopez-Escobar, E. G.K., Infinite rules in finite systems, (Arruda, A. I.; da Costa, N. C.A.; Chuaqui, R., Non-Classical Logics, Model Theory and Computability (1977), North-Holland: North-Holland Amsterdam) · Zbl 0386.03026 |
| [2] | Mirkowska, G.; Salwicki, A., Algorithmic Logic (1987), Dordrecht: Dordrecht Warsaw · Zbl 0648.03018 |
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