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References
Ajtai, M. Σ 11 -formulae on finite structures. Annals of Pure and Applied Logic, 24(1),(1983).
Bel’tyukov,A. A computer description and a hierarchy of initial Grzegorczyk classes. Zap.Navcu.Sem.Leningrad Otdel Mat. Inst.Steklov (LOMI) 88, (1979).
Gaifman, H. & Dimitracopoulos, C. Fragments of Peano’s Arithmetic and the MRDP theorem, Logic and Algorithmic, Monographie No 30 de L’Enseignement Mathematique
Goad, C. Duplicated Notes on the pigeon hole principle.
Hicks, J. A machine characterization of quantification and primitive recursion with applications to low level complexity classes. Ph.D. Thesis, Oxford University (Submitted 1983).
Nepomnjascii, V. Rudimentary predicates and Turing calculations. Soviet Math.Dokl. 11, No 6 (1970).
Paris, J. & Dimitracopoulos, C. Truth definitions for Δ0 formulae. Logic and Algorithmic, Monographie No 30 de L’Enseignement Mathematique.
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.
Ritchie, R. Classes of predictably computable functions. TAMS 106 (1963).
Wilkie, A. & Paris, J. On the schema of induction for bounded arithmetic formulas. (To appear).
Woods, A. Some problems in logic and number theory and their connections. Ph.D. Thesis, Manchester University (1981)
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.
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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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