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An addition to Rosser's theorem

Published online by Cambridge University Press:  12 March 2014

Henryk Kotlarski*
Affiliation:
Instytut Matematyki i Fizyki WSRP, ul Orlicz-Dreszera 19/21, 08-110 Siedlce, Poland, E-mail: hkl@impan.impan.gov.pl

Abstract

For a primitive recursive consistent and strong enough theory T we construct an independent statement which has some clear metamathematical meaning.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1996

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References

REFERENCES

[1]Feferman, S., Arithmetization of metamathematics in a general setting, Fundamenta Mathematica, vol. 49 (1960), pp. 3592.CrossRefGoogle Scholar
[2]Hàjek, P. and Pudlàk, P., Metamathematics of first order arithmetic, Perspectives in Mathematical Logic, Springer-Verlag, 1993.CrossRefGoogle Scholar
[3]Kaye, R., Models of Peano arithmetic, Oxford Logic Guides, Oxford University Press, 1991.CrossRefGoogle Scholar
[4]Kotlarski, H., On the incompleteness theorems, this Journal, vol. 59 (1994), no. 4, pp. 14141419.Google Scholar
[5]Kotlarski, H., Krajewski, S., and Lachlan, A. H., Construction of satisfaction classes for non-standard models, Canadian Mathematics Bulletin, vol. 24 (1981), no. 3, pp. 283293.CrossRefGoogle Scholar
[6]Krajíček, J., On the number of steps in proofs, Annals of Pure and Applied Logic, vol. 42 (1989), no. 1, pp. 2143.Google Scholar
[7]Krajíček, J. and Pudlàk, P., On the structure of initial segments of models of arithmetic, Archive for Mathematical Logic, vol. 28 (1989), pp. 9198.CrossRefGoogle Scholar
[8]Shoenfield, J. R., Mathematical logic, Addison-Wesley, 1967.Google Scholar
[9]Smoryński, C., The incompleteness theorems, Handbook of mathematical logic (Barwise, J., editor). North-Holland, 1977, pp. 821865.CrossRefGoogle Scholar
[10]Solovay, R. M., Injecting inconsistencies into models of PA, Annals of Pure and Applied Logic, vol. 44 (1989), pp. 101132.CrossRefGoogle Scholar