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Burgess’ PV is Robinson’s Q

  • Mihai Ganea (a1)


In [2] John Burgess describes predicative versions of Frege's logic and poses the problem of finding their exact arithmetical strength. I prove here that PV, the simplest such theory, is equivalent to Robinson's arithmetical theory Q.



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[1]Boolos, G. S., Burgess, J. P., and Jeffrey, R. C., Computability and logic, 4th ed., Cambridge University Press, 2002.
[2]Burgess, J. P., Fixing Frege, Princeton University Press, 2005.
[3]Buss, S., Nelson's work on logic and foundations and other reflections on foundations of mathematics, Diffusion, quantum theory, and radically elementary mathematics (Faris, W. G., editor), Mathematical Notes, vol. 47, Princeton University Press, 2006, pp. 183–208.
[4]Cutland, N. J., Computability—an introduction to recursive function theory, Cambridge University Press, 1980.
[5]Feferman, S., Predicativity, The Oxford handbook of philosophy of mathematics and logic (Shapiro, S., editor), Oxford University Press, 2005, pp. 590–624.
[6]Goldfarb, W., Poincaré against the logicists, History and philosophy of mathematics (Aspray, W. and Kitcher, P., editors), Minnesota Studies in the Philosophy of Science, vol. XI, University of Minnesota Press, Minneapolis, 1988, pp. 61–81.
[7]Hájek, P. and Pudlák, P., Metamathematics of first-order arithmetic, Springer-Verlag, 1993.
[8]Krajiček, J., Bounded arithmetic, propositional logic, and complexity theory, Encyclopedia of Mathematics and Its Applications, vol. 60, Cambridge University Press, 1995.
[9]Nelson, E., Predicative arithmetic, Mathematical Notes, vol. 32, Princeton University Press, 1986.
[10]Visser, A., The predicative Frege hierarchy, preprint (09 2006), 42 p., available online at
[11]Wilkie, A. J., On sentences interpretable in systems of arithmetic, Logic Colloquium ’84 (Paris, J. B., Wilkie, A. J., and Wilmers, G. M., editors), Elsevier Science Publishers B. V., North Holland, 1986, pp. 329–342.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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