Skip to main content Accessibility help




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.



Hide All
[1]Baldwin, J. T., Fundamentals of Stability Theory, Springer, Berlin, 1988.
[2]Baldwin, J. T. and Shelah, S., The structure of saturated free algebras. Algebra Universalis, vol. 17 (1983), pp. 191199.
[3]Burris, S. and Sankappanavar, H. P., A Course in Universal Algebra, available online at∼snburris/htdocs/UALG/univ-algebra2012.pdf.
[4]Lascar, D., Stability in Model Theory, John Wiley & Sons, New York, incorporated, 1987.
[5]Lascar, D. and Poizat, B., An introduction to forking, this Journal, vol. 44 (1979), pp. 330350.
[6]Makkai, M., A survey of basic stability theory, with particular emphasis on orthogonality and regular types. Israel Journal of Mathematics, vol. 44 (1979), pp. 330350.
[7]Mariou, B., Modèles saturés et modèles engendrés par des indiscernables, this Journal, vol. 66 (2001), pp. 325348.
[8]Perin, C. and Sklinos, R., Forking and JSJ decompositions in the Free Group. Journal of the European Mathematical Society (JEMS), to appear.
[9]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. 1022.
[10]Pillay, A., Geometric Stability Theory, Oxford University Press, New York, 1996.
[11]Pillay, A., Forking in the free group. Journal of the Institute of Mathematics of Jussieu, vol. 7 (2008), pp. 375389.
[12]Poizat, B., Le Groupe Libre est-il Stable?, Seminarberichte 93-1, Humboldt Universität zu Berlin, pp. 169176.
[13]Shelah, S., Classification Theory: And the Number of Non-Isomorphic Models, Elsevier, Amsterdam, 1990.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Bulletin of Symbolic Logic
  • ISSN: 1079-8986
  • EISSN: 1943-5894
  • URL: /core/journals/bulletin-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed