A viewpoint on amalgamation classes

Silvia Barbina; Domenico Zambella

Commentationes Mathematicae Universitatis Carolinae (2010)

  • Volume: 51, Issue: 4, page 681-691
  • ISSN: 0010-2628

Abstract

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We give a self-contained introduction to universal homogeneous models (also known as rich models) in a general context where the notion of morphism is taken as primitive. We produce an example of an amalgamation class where each connected component has a saturated rich model but the theory of the rich models is not model-complete.

How to cite

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Barbina, Silvia, and Zambella, Domenico. "A viewpoint on amalgamation classes." Commentationes Mathematicae Universitatis Carolinae 51.4 (2010): 681-691. <http://eudml.org/doc/246403>.

@article{Barbina2010,
abstract = {We give a self-contained introduction to universal homogeneous models (also known as rich models) in a general context where the notion of morphism is taken as primitive. We produce an example of an amalgamation class where each connected component has a saturated rich model but the theory of the rich models is not model-complete.},
author = {Barbina, Silvia, Zambella, Domenico},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {model theory; universal homogeneous model; model companion; amalgamation class; universal homogeneous model; model companion; amalgamation class},
language = {eng},
number = {4},
pages = {681-691},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A viewpoint on amalgamation classes},
url = {http://eudml.org/doc/246403},
volume = {51},
year = {2010},
}

TY - JOUR
AU - Barbina, Silvia
AU - Zambella, Domenico
TI - A viewpoint on amalgamation classes
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2010
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 51
IS - 4
SP - 681
EP - 691
AB - We give a self-contained introduction to universal homogeneous models (also known as rich models) in a general context where the notion of morphism is taken as primitive. We produce an example of an amalgamation class where each connected component has a saturated rich model but the theory of the rich models is not model-complete.
LA - eng
KW - model theory; universal homogeneous model; model companion; amalgamation class; universal homogeneous model; model companion; amalgamation class
UR - http://eudml.org/doc/246403
ER -

References

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  6. Hrushovski E., 10.1016/0168-0072(93)90171-9, Ann. Pure Appl. Logic 62 (1993), no. 2, 147–166. Zbl0804.03020MR1226304DOI10.1016/0168-0072(93)90171-9
  7. Kueker D.W., Laskowski M.C., 10.1305/ndjfl/1093636094, Notre Dame J. Formal Logic 33 (1992), no. 2, 175–183. Zbl0768.03010MR1167973DOI10.1305/ndjfl/1093636094
  8. Lascar D., 10.1007/BF01370694, Arch. Math. Logic 31 (1991), no. 1, 55–68. Zbl0766.03022MR1126353DOI10.1007/BF01370694
  9. Poizat B., 10.2307/2586634, J. Symbolic Logic 64 (1999), no. 3, 1339–1355. Zbl0938.03058MR1779766DOI10.2307/2586634
  10. Zambella D., Krull dimension of types in a class of first-order theories, Turkish J. Math.(to appear). MR2839726

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