Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-16T13:14:18.176Z Has data issue: false hasContentIssue false
  • English
  • Français

SATURATED FREE ALGEBRAS REVISITED

Published online by Cambridge University Press:  15 September 2015

ANAND PILLAY  and
RIZOS SKLINOS
ANAND PILLAY
Affiliation:
UNIVERSITY OF NOTRE DAME IN 46556, USAE-mail: apillay@nd.edu
RIZOS SKLINOS
Affiliation:
UNIVERSITÉ LYON 1FRANCEE-mail: rizozs@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

We give an exposition of results of Baldwin–Shelah [2] on saturated free algebras, at the level of generality of complete first order theories T with a saturated model M which is in the algebraic closure of an indiscernible set. We then make some new observations when M is a saturated free algebra, analogous to (more difficult) results for the free group, such as a description of forking.

Keywords

03C0503C45free algebrasforking independence
Type
Articles
Information
Bulletin of Symbolic Logic , Volume 21 , Issue 3 , September 2015 , pp. 306 - 318
Copyright
Copyright © The Association for Symbolic Logic 2015 

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

Baldwin, J. T., Fundamentals of Stability Theory, Springer, Berlin, 1988.CrossRefGoogle Scholar
Baldwin, J. T. and Shelah, S., The structure of saturated free algebras. Algebra Universalis, vol. 17 (1983), pp. 191–199.CrossRefGoogle Scholar
Burris, S. and Sankappanavar, H. P., A Course in Universal Algebra, available online at http://www.math.uwaterloo.ca/∼snburris/htdocs/UALG/univ-algebra2012.pdf.CrossRefGoogle Scholar
Lascar, D., Stability in Model Theory, John Wiley & Sons, New York, incorporated, 1987.Google Scholar
Lascar, D. and Poizat, B., An introduction to forking, this Journal, vol. 44 (1979), pp. 330–350.Google Scholar
Makkai, M., A survey of basic stability theory, with particular emphasis on orthogonality and regular types. Israel Journal of Mathematics, vol. 44 (1979), pp. 330–350.Google Scholar
Mariou, B., Modèles saturés et modèles engendrés par des indiscernables, this Journal, vol. 66 (2001), pp. 325–348.Google Scholar
Perin, C. and Sklinos, R., Forking and JSJ decompositions in the Free Group. Journal of the European Mathematical Society (JEMS), to appear.Google Scholar
Pillay, A., The models of a non-multidimensional ω-stable theory, Groupe d’étude de théories stables (1980–1982) (Poizat, Bruno, editor), vol. 3 (1983), pp. 10–22.Google Scholar
Pillay, A., Geometric Stability Theory, Oxford University Press, New York, 1996.CrossRefGoogle Scholar
Pillay, A., Forking in the free group. Journal of the Institute of Mathematics of Jussieu, vol. 7 (2008), pp. 375–389.CrossRefGoogle Scholar
Poizat, B., Le Groupe Libre est-il Stable?, Seminarberichte 93-1, Humboldt Universität zu Berlin, pp. 169–176.Google Scholar
Shelah, S., Classification Theory: And the Number of Non-Isomorphic Models, Elsevier, Amsterdam, 1990.Google Scholar