Abstract.
We give a short proof of a theorem of Kanovei on separating induction and collection schemes for Σ n formulas using families of subsets of countable models of arithmetic coded in elementary end extensions.
Similar content being viewed by others
References
Hájek, P., Pudlák, P.: Metamathematics of first-order arithmetic. Perspectives in Mathematical Logic. Springer-Verlag, 1998. Second printing
Kanovei, V.: On ‘‘star’’ schemata of Kossak and Paris, volume~12 of Lecture Notes Logic, pp. 101–114. Springer, Berlin, 1998
Kaye, R.: Models of Peano Arithmetic, volume~15 of Oxford Logic Guides. Clarendon Press, Oxford, 1991
Kirby, L.A.S., Paris, J.B.: Initial segments of models of Peano’s axioms, pp. 211–226. Lecture Notes in Math., Vol. 619, Springer-Verlag, 1977
Kossak, R.: Models with the ω property. J. Symb. Logic 54(1), 177–189 (1989)
Kossak, R.: On extensions of models of strong fragments of arithmetic. Proc. Am. Math. Soc. 108(1), 223–232 (1990)
Kossak, R., Paris, J.B.: Subsets of models of arithmetic. Arch. Math. Logic 32(1), 65–73 (1992)
Paris, J.B.: A hierarchy of cuts in models of arithmetic. Lecture Notes in Math. vol. 834, pp. 312–337, Springer-Verlag, 1980
Paris, J.B.: Some conservation results for fragments of arithmetic, volume Lecture Notes in Math. vol. 890, pp. 251–262, Springer-Verlag, 1981
Author information
Authors and Affiliations
Corresponding author
Additional information
Mathematics Subject Classification (2000): 03C62
Rights and permissions
About this article
Cite this article
Kossak, R. A note on a theorem of Kanovei. Arch. Math. Logic 43, 565–569 (2004). https://doi.org/10.1007/s00153-004-0218-2
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00153-004-0218-2