Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-19T10:46:59.668Z Has data issue: false hasContentIssue false
  • English
  • Français

Burgess’ PV is Robinson’s Q

Published online by Cambridge University Press:  12 March 2014

Mihai Ganea
Mihai Ganea*
Affiliation:
Department of Philosophy, University of Illinois at Chicago, Chicago, Illinois 60607-7114, USA, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 2 , June 2007 , pp. 619 - 624
Copyright
Copyright © Association for Symbolic Logic 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Boolos, G. S., Burgess, J. P., and Jeffrey, R. C., Computability and logic, 4th ed., Cambridge University Press, 2002.CrossRefGoogle Scholar
[2]Burgess, J. P., Fixing Frege, Princeton University Press, 2005.CrossRefGoogle Scholar
[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.Google Scholar
[4]Cutland, N. J., Computability—an introduction to recursive function theory, Cambridge University Press, 1980.Google Scholar
[5]Feferman, S., Predicativity, The Oxford handbook of philosophy of mathematics and logic (Shapiro, S., editor), Oxford University Press, 2005, pp. 590–624.Google Scholar
[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.Google Scholar
[7]Hájek, P. and Pudlák, P., Metamathematics of first-order arithmetic, Springer-Verlag, 1993.CrossRefGoogle Scholar
[8]Krajiček, J., Bounded arithmetic, propositional logic, and complexity theory, Encyclopedia of Mathematics and Its Applications, vol. 60, Cambridge University Press, 1995.CrossRefGoogle Scholar
[9]Nelson, E., Predicative arithmetic, Mathematical Notes, vol. 32, Princeton University Press, 1986.CrossRefGoogle Scholar
[10]Visser, A., The predicative Frege hierarchy, preprint (09 2006), 42 p., available online at http://www.phil.uu.nl/preprints/lgps/index.html.Google Scholar
[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.Google Scholar