Archive for Mathematical Logic

, Volume 33, Issue 4, pp 265–281 | Cite as

The prime number theorem and fragments ofP A

  • C. Cornaros
  • C. Dimitracopoulos


We show that versions of the prime number theorem as well as equivalent statements hold in an arbitrary model of0+exp.


Mathematical Logic Prime Number Equivalent Statement Prime Number Theorem Arbitrary Model 
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  1. 1.
    Berarducci A., Intrigila, B.: Combinatorial principles in elementary number theory. Ann. Pure Appl. Logic55, 35–50 (1991)Google Scholar
  2. 2.
    Clote, P., Hájek P., Paris, J.: On some formalized conservation results in arithmetic. Arch. Math. Logic30, 201–218 (1990)Google Scholar
  3. 3.
    Cornaros, Ch.: Ph. D. thesis. University of Crete, to appearGoogle Scholar
  4. 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. 5.
    Hájek, P., Pudlák, P.: Metamathematics of First-Order Arithmetic. Springer-Verlag, Berlin, 1992Google Scholar
  6. 6.
    Macintyre, A.J.: The strength of weak systems. In: Proc. 11th Intern. Wittgenstein Symp., Kirchberg/Wechsel, Austria, 1986 (Hölder-Pichler-Tempsky, Vienna, 1987), 43–59Google Scholar
  7. 7.
    Paris, J., Kirby, L.A.S.: n-Collection schemas in arithmetic. Logic Colloquium '77, North-Holland (1978), 199–209Google Scholar
  8. 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. 9.
    Shapiro, H.N.: Introduction to the theory of numbers. Wiley-Interscience, New York, 1983Google Scholar
  10. 10.
    Woods, A.R.: Some problems in logic and number theory, and their connections. Ph. D. thesis, University of Manchester, 1981Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • C. Cornaros
    • 1
  • C. Dimitracopoulos
    • 1
  1. 1.Department of MathematicsUniversity of CreteIraklioGreece

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