Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-11T06:55:55.189Z Has data issue: false hasContentIssue false
  • English
  • Français

An analytic completeness theorem for logics with probability quantifiers

Published online by Cambridge University Press:  12 March 2014

Douglas N. Hoover
Douglas N. Hoover*
Affiliation:
Department of Mathematics and Statistics, Queens University, Kingston, Ontario K71 3N6, Canada
Get access Rights & Permissions [Opens in a new window]

Abstract

We give a completeness theorem for a logic with probability quantifiers which is equivalent to the logics described in a recent survey paper of Keisler [K]. This result improves on the completeness theorems in [K] in that it works for languages with function symbols and produces a model whose universe is an analytic subset of the real line, and whose relations and functions are Borel relative to this universe.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 52 , Issue 3 , September 1987 , pp. 802 - 816
Copyright
Copyright © Association for Symbolic Logic 1987

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.)

Footnotes

1

This research was supported by an NSERC operating grant. The author is an NSERC University Research Fellow.

2

We thank H. J. Keisler for pointing out an error in the original statement of the Horn Lemma.

References

REFERENCES

[F] Falkner, Neil, Generalizations of analytic and standard measurable spaces, Mathematica Scandinavica, vol. 49 (1981), pp. 283–301.CrossRefGoogle Scholar
[Hl] Hoover, D. N., Probability logic, Annals of Mathematical Logic, vol. 14 (1978), pp. 287–313.CrossRefGoogle Scholar
[H2] Hoover, D. N., A normal form theorem for Lω1P, with applications, this Journal, vol. 47 (1982), pp. 605–624.Google Scholar
[K] Keisler, H.J., Probability quantifiers, Model-theoretic logics (Barwise, J. and Feferman, S., editors), Springer-Verlag, Berlin, 1985, pp. 509–556.Google Scholar
[S] Steinhorn, C. I., Borel structures and measure and category logics, Model-theoretic logics (Barwise, J. and Feferman, S., editors), Springer-Verlag, Berlin, 1985, pp. 579–596.Google Scholar
[V] von Neumann, J., Einige Sätze über messbare Abbildungen, Annals of Mathematics, ser. 2, vol. 33 (1932), pp. 574–586.CrossRefGoogle Scholar