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SATURATED FREE ALGEBRAS REVISITED

  • ANAND PILLAY (a1) and RIZOS SKLINOS (a2)
Abstract
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.

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[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 http://www.math.uwaterloo.ca/∼snburris/htdocs/UALG/univ-algebra2012.pdf.
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[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.
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Bulletin of Symbolic Logic
  • ISSN: 1079-8986
  • EISSN: 1943-5894
  • URL: /core/journals/bulletin-of-symbolic-logic
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