Skip to main content
SpringerLink
Log in

The prime number theorem and fragments ofP A

  • Published:
Archive for Mathematical Logic Aims and scope Submit manuscript

Summary

We show that versions of the prime number theorem as well as equivalent statements hold in an arbitrary model ofIΔ 0+exp.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Berarducci A., Intrigila, B.: Combinatorial principles in elementary number theory. Ann. Pure Appl. Logic55, 35–50 (1991)

    Google Scholar 

  2. Clote, P., Hájek P., Paris, J.: On some formalized conservation results in arithmetic. Arch. Math. Logic30, 201–218 (1990)

    Google Scholar 

  3. Cornaros, Ch.: Ph. D. thesis. University of Crete, to appear

  4. Gaifman, H., Dimitracopoulos, C.: Fragments of Peano's arithmetic and the MRDP theorem. Logic and Algorithmic, Monograph. Enseign. Math.30, 187–206 (1982)

    Google Scholar 

  5. Hájek, P., Pudlák, P.: Metamathematics of First-Order Arithmetic. Springer-Verlag, Berlin, 1992

    Google Scholar 

  6. Macintyre, A.J.: The strength of weak systems. In: Proc. 11th Intern. Wittgenstein Symp., Kirchberg/Wechsel, Austria, 1986 (Hölder-Pichler-Tempsky, Vienna, 1987), 43–59

    Google Scholar 

  7. Paris, J., Kirby, L.A.S.:∑ n -Collection schemas in arithmetic. Logic Colloquium '77, North-Holland (1978), 199–209

  8. Paris, J.B., Wilkie, A.J., Woods, A.R.: Provability of the pigeonhole principle and the existence of infinitely many primes. J. Symbolic Logic53, 1235–1244 (1988)

    Google Scholar 

  9. Shapiro, H.N.: Introduction to the theory of numbers. Wiley-Interscience, New York, 1983

    Google Scholar 

  10. Woods, A.R.: Some problems in logic and number theory, and their connections. Ph. D. thesis, University of Manchester, 1981

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Crete, 714 09, Iraklio, Greece

    C. Cornaros & C. Dimitracopoulos

Authors
  1. C. Cornaros
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Dimitracopoulos
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

A part of the preparation of this paper was done while the authors were visiting the University of Oxford in the spring of 1992; their visit was partially supported by the University of Crete (grant no. 185) and the British Council. The authors thank Drs. R. Kaye and A. Wilkie for useful discussions and the Mathematical Institute of the University of Oxford for their hospitality; they also thank Dr. K. Skandalis for pointing out an error in an earlier proof of Theorem 3.3 and the two referees, for suggesting Lemma 1.13 as a common generalization of some earlier Lemmas and for many other comments, which helped to improve this paper

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cornaros, C., Dimitracopoulos, C. The prime number theorem and fragments ofP A . Arch Math Logic 33, 265–281 (1994). https://doi.org/10.1007/BF01270626

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01270626

Keywords

Search

Navigation