Hostname: page-component-cb9f654ff-hn9fh Total loading time: 0 Render date: 2025-08-12T17:12:06.586Z Has data issue: false hasContentIssue false
  • English
  • Français

GENERALIZED AMALGAMATION AND HOMOGENEITY

Published online by Cambridge University Press:  09 November 2017

DANIEL PALACÍN
DANIEL PALACÍN*
Affiliation:
MATHEMATISCHES INSTITUT UNIVERSITÄT MÜNSTER EINSTEINSTRASSE 62 48149 MÜNSTER, GERMANY E-mail: daniel.palacin@mail.huji.ac.il
Rights & Permissions [Opens in a new window]

Abstract

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.

In this paper we shall prove that any 2-transitive finitely homogeneous structure with a supersimple theory satisfying a generalized amalgamation property is a random structure. In particular, this adapts a result of Koponen for binary homogeneous structures to arbitrary ones without binary relations. Furthermore, we point out a relation between generalized amalgamation, triviality and quantifier elimination in simple theories.

Keywords

03C45model theoryrandom structuresimple theoryamalgamation property

Information

Type
Articles
Information
The Journal of Symbolic Logic , Volume 82 , Issue 4 , December 2017 , pp. 1409 - 1421
Copyright
Copyright © The Association for Symbolic Logic 2017 

References

REFERENCES

Buechler, S., Essential stability theory, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1996.Google Scholar
Casanovas, E., Simple Theories and Hyperimaginaries, Lecture Notes in Logic, Cambridge University Press, Cambridge, 2011.CrossRefGoogle Scholar
Conant, G., An axiomatic approach to free amalgamation, this Journal, to appear.Google Scholar
Goode, J. B., Some trivial considerations, this Journal, vol. 56 (1991), no. 2, pp. 624–631.Google Scholar
Hrushovski, E., Simplicity and the lascar group, unpublished notes, 1997.Google Scholar
Kim, B., Simplicity Theory, Oxford Logic Guides, vol. 53, Oxford Science Publications, Oxford, 2013.Google Scholar
Koponen, V., Binary simple homogeneous structures are supersimple with finite rank . Proceedings of the American Mathematical Society, vol. 144 (2016), no. 4, pp. 1745–1759.Google Scholar
Koponen, V., Binary primitive homogeneous one-based structures, this Journal, to appear.Google Scholar
Koponen, V., Homogeneous 1-based structures and interpretability in random structures . Mathematical Logic Quarterly, to appear.Google Scholar
López, A. A., Omega-categorical simple theories, Ph.D. thesis, University of Leeds, 2013.Google Scholar
Macpherson, D., A survey of homogeneous structures . Discrete Math. Discrete Mathematics, vol. 311 (2011), no. 15, pp. 1599–1634.Google Scholar
Macpherson, D. and Tent, K., Simplicity of some automorphism groups . Journal of Algebra, vol. 342 (2011), no. 1, pp. 40–52.Google Scholar
Martin-Pizarro, A., Baudisch, A., and Ziegler, M., A model theoretic study of right-angled buildings . Journal of the European Mathematical Society, to appear.Google Scholar
Wagner, F. O., Simple Theories, Mathematics and Iits Applications, vol. 503, Kluwer Academic Publishers, Dordrecht, 2000.Google Scholar