Hostname: page-component-7dd5485656-zlgnt Total loading time: 0 Render date: 2025-10-29T21:02:14.458Z Has data issue: false hasContentIssue false
  • English
  • Français

Some remarks on initial segments in models of Peano arithmetic

Published online by Cambridge University Press:  12 March 2014

Henryk Kotlarski
Henryk Kotlarski*
Affiliation:
Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada Instytut Zastosowan Matematykii Statystyki Sggw-Ar, Ul. Nowoursynowska 166, 02-766 Warsaw, Poland
Get access Rights & Permissions [Opens in a new window]

Abstract

If M ⊨ PA (= Peano Arithmetic), we set AM = {N ⊂eM: N ⊨ PA} and study this family.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 49 , Issue 3 , September 1984 , pp. 955 - 960
Copyright
Copyright © Association for Symbolic Logic 1984

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]Dmitracopoulos, C., MRDP theorem and fragments of arithmetic, Doctoral thesis, Manchester, 1980.Google Scholar
[2]Gaifman, H., A note on models and submodels of arithmetic, Conference in mathematic logic—ondon '70, Lecture Notes in Mathematics, vol. 255, Springer-Verlag, Berlin, 1972, pp. 128–144.CrossRefGoogle Scholar
[3]Kirby, L., Initial segments of models of arithmetic, Doctoral thesis, Manchester, 1977.CrossRefGoogle Scholar
[4]Kotlarski, H., On elementary cuts in models of arithmetic, Fundamenta Mathematicae, vol. 115 (1983), pp. 27–31.CrossRefGoogle Scholar
[5]Kotlarski, H., On elementary cuts in recursively saturated models of arithmetic, Fundamenta Mathematicae, vol. 120 (to appear).Google Scholar
[6]Lessan, H., Models of arithmetic, Doctoral thesis, Manchester, 1978.Google Scholar
[7]Paris, J., Some independence results for Peano arithmetic, this Journal, vol. 43 (1978), pp. 725–731.Google Scholar
[8]Paris, J. and Harrington, L., A mathematical independence in Peano arithmetic, Handbook of mathematical logic, North-Holland, Amsterdam, 1977, pp. 1133–1142.CrossRefGoogle Scholar
[9]Smoryński, C., Recursively saturated nonstandard models of arithmetic, this Journal, vol. 46 (1981), pp. 259–286.Google Scholar