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Counting problems in bounded arithmetic

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Methods in Mathematical Logic

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1130))

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References

  1. Ajtai, M. Σ 11 -formulae on finite structures. Annals of Pure and Applied Logic, 24(1),(1983).

    Google Scholar 

  2. Bel’tyukov,A. A computer description and a hierarchy of initial Grzegorczyk classes. Zap.Navcu.Sem.Leningrad Otdel Mat. Inst.Steklov (LOMI) 88, (1979).

    Google Scholar 

  3. Gaifman, H. & Dimitracopoulos, C. Fragments of Peano’s Arithmetic and the MRDP theorem, Logic and Algorithmic, Monographie No 30 de L’Enseignement Mathematique

    Google Scholar 

  4. Goad, C. Duplicated Notes on the pigeon hole principle.

    Google Scholar 

  5. Hicks, J. A machine characterization of quantification and primitive recursion with applications to low level complexity classes. Ph.D. Thesis, Oxford University (Submitted 1983).

    Google Scholar 

  6. Nepomnjascii, V. Rudimentary predicates and Turing calculations. Soviet Math.Dokl. 11, No 6 (1970).

    Google Scholar 

  7. Paris, J. & Dimitracopoulos, C. Truth definitions for Δ0 formulae. Logic and Algorithmic, Monographie No 30 de L’Enseignement Mathematique.

    Google Scholar 

  8. Paris, J. & Wilkie, A. Δ0 sets and induction. Open Days in Model Theory and Set Theory, Proceedings of the 1981 Jadwisin (Poland) Logic Conference, Ed. Guzicki, Marek, Pelc, Rauszer.

    Google Scholar 

  9. Ritchie, R. Classes of predictably computable functions. TAMS 106 (1963).

    Google Scholar 

  10. Wilkie, A. & Paris, J. On the schema of induction for bounded arithmetic formulas. (To appear).

    Google Scholar 

  11. Woods, A. Some problems in logic and number theory and their connections. Ph.D. Thesis, Manchester University (1981)

    Google Scholar 

  12. Furst, M., Saxe, J.B.& Sipser, M. Parity, circuits and the polynomial-time hierarchy. IEEE Foundations of Computer Science (22nd Symposium). (1981), pp. 260–270.

    Google Scholar 

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Carlos Augusto Di Prisco

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© 1985 Springer-Verlag

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Paris, J., Wilkie, A. (1985). Counting problems in bounded arithmetic. In: Di Prisco, C.A. (eds) Methods in Mathematical Logic. Lecture Notes in Mathematics, vol 1130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075316

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  • DOI: https://doi.org/10.1007/BFb0075316

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15236-1

  • Online ISBN: 978-3-540-39414-3

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