Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-14T06:57:11.870Z Has data issue: false hasContentIssue false
  • English
  • Français

Absolutely Free Algebras in a Topos Containing an Infinite Object

Published online by Cambridge University Press:  20 November 2018

D. Schumacher
D. Schumacher*
Affiliation:
Department of Mathematics, Acadia University, Wolfville, Nova Scotia, Canada
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This note confirms that the existence proof for absolutely free algebras originated by Dedekind in [2] and completely developed for instance in [4] can still be carried out in a topos containing an infinite object i.e. an object N for which N ≃ N+1 if the type of the algebras considered is finite, pointed and internally projective i.e. is a finite sequence of objects, (Ij)i≤j≤k for which the functors ( )Ij preserve epimorphisms and each of which has a global section.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 3 , 01 September 1976 , pp. 323 - 328
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Cohn, P. M., Universal Algebra, Harper and Row, 1965.Google Scholar
2. Dedekind, R., Was sind und was sollen die Zahlen? 1871.Google Scholar
3. Freyd, P., Aspects of topoi, Bull. Austral. Math. Soc, Vol. 7 (1972), p. 1–76.Google Scholar
4. Kerkhoff, R., Eine Konstruktion freier Algebren, Math. Annalen, Vol. 158 (1965), p. 109–112.Google Scholar
5. Lesaflre, B., Structures algébriques dans les topos élémentaires, C. R. Acad. Se. Paris, t277 (8 octobre 1973), p. 663–666.Google Scholar
6. Mikkelsen, Ch. J., On the internal completeness of elementary topoi, Tagungsbericht 30/1973, Mathematisches Forschungsinstitut Oberwolfach.Google Scholar
7. Schumacher, D., Peanoalgebras in a topos containing a natural number object, Tagungsbericht 30/1973, Mathematisches Forschungsinstitut Oberwolfach.Google Scholar