Hostname: page-component-cb9f654ff-65tv2 Total loading time: 0 Render date: 2025-08-01T10:06:33.379Z Has data issue: false hasContentIssue false
  • English
  • Français

The model-theoretic ordinal analysis of theories of predicative strength

Published online by Cambridge University Press:  12 March 2014

Jeremy Avigad  and
Richard Sommer
Jeremy Avigad
Affiliation:
Department of Philosophy, Carnegie Mellon University, Pittsburgh, Pa 15213, USA E-mail: avigad@cmu.edu
Richard Sommer
Affiliation:
Center for the Study of Language and Information, Stanford University, Stanford, CA 94305-4115, USA E-mail: sommer@csli.stanford.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We use model-theoretic methods described in [3] to obtain ordinal analyses of a number of theories of first- and second-order arithmetic, whose proof-theoretic ordinals are less than or equal to Γ0.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 1 , March 1999 , pp. 327 - 349
Copyright
Copyright © Association for Symbolic Logic 1999

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.)

Article purchase

Temporarily unavailable

References

REFERENCES

[1]Aczel, Peter, An introduction to inductive definitions, The handbook of mathematical logic (Barwise, J., editor), North-Holland, 1977, pp. 739–782.Google Scholar
[2]Avigad, Jeremy, On the relationship between ATR0 and , this Journal, vol. 61 (1996), pp. 768–779.Google Scholar
[3]Avigad, Jeremy and Sommer, Richard, A model-theoretic approach to ordinal analysis, Bulletin of Symbolic Logic, vol. 3 (1997), pp. 17–52.CrossRefGoogle Scholar
[4]Feferman, Solomon, Systems of predicative analysis, this Journal, vol. 29 (1964), pp. 1–30.Google Scholar
[5]Feferman, Solomon, Iterated inductive fixed-point theories: application to hancock's conjecture, Patras logic symposium (Metakides, G., editor), North-Holland, 1982.Google Scholar
[6]Friedman, Harvey, Iterated inductive definitions and , Inflationism and proof theory (Kino, A.et al., editors), North-Holland, 1970, pp. 435–442.Google Scholar
[7]Friedman, Harvey, McAloon, Kenneth, and Simpson, Stephen, A finite combinatorial principle which is equivalent to the 1-consistency of predicative analysis, Patras logic symposium (Metakides, G., editor), North-Holland, 1982, pp. 197–230.Google Scholar
[8]Pohlers, Wolfram, Proof theory: an introduction, Lecture Notes in Mathematics, vol. 1407, Springer-Verlag, 1989.CrossRefGoogle Scholar
[9]Simpson, Stephen, Subsystems of Z2 and reverse mathematics, appendix to Gaisi Takeuti, Proof theory, second edition, North-Holland, 1987.Google Scholar
[10]Simpson, Stephen, On the strength of König's duality theorem of countable bipartite graphs, this Journal, vol. 59 (1994), pp. 113–123.Google Scholar
[11]Simpson, Stephen, Subsystems of second order arithmetic, Springer-Verlag, 1998.Google Scholar
[12]Sommer, Richard, Transfinite induction within Peano arithmetic, Annals of Pure and Applied Logic, vol. 76 (1995), pp. 231–289.CrossRefGoogle Scholar