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WEAK SATURATION AND WEAK AMALGAMATION PROPERTY

Published online by Cambridge University Press:  04 July 2019

IVAN DI LIBERTI
IVAN DI LIBERTI*
Affiliation:
DEPARTMENT OF MATHEMATICS AND STATISTICS MASARYK UNIVERSITY, FACULTY OF SCIENCES KOTLÁŘSKÁ 2, 611 37BRNO, CZECH REPUBLIC E-mail: [email protected]
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Abstract

We study the two model-theoretic concepts of weak saturation and weak amalgamation property in the context of accessible categories. We relate these two concepts providing sufficient conditions for existence and uniqueness of weakly saturated objects of an accessible category ${\cal K}$. We discuss the implications of this fact in classical model theory.

Keywords

18C3503C52Fraïssé classesaccessible categoriescategorical model theoryweak amalgamation propertyweak saturation
Type
Articles
Information
The Journal of Symbolic Logic , Volume 84 , Issue 3 , September 2019 , pp. 929 - 936
Copyright
Copyright © The Association for Symbolic Logic 2019 

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References

REFERENCES

Adamek, J. and Rosicky, J., Locally Presentable and Accessible Categories, London Mathematical Society Lecture Note Series, vol. 189, Cambridge University Press, Cambridge, 1994.Google Scholar
Ivanov, A. A., Generic expansions of ω-categorical structures and semantics of generalized quantifiers, this Journal, vol. 64 (1999), no. 2, pp. 775–789.Google Scholar
Kechris, A. S. and Rosendal, C., Turbulence, amalgamation, and generic automorphisms of homogeneous structures. Proceedings of the London Mathematical Society, vol. 94 (2007), no. 2, pp. 302–350.Google Scholar
Kubiś, W., Fraïssś sequences: Category-theoretic approach to universal homogeneous structures. Annals of Pure and Applied Logic, vol. 165 (2014), no. 11, pp. 1755–1811.Google Scholar
Kubiś, W., Weak Fraisse categories, preprint, 2017, arXiv:1712.03300.Google Scholar
Rosický, J., Accessible categories, saturation and categoricity, this Journal, vol. 62 (1997), no. 3, pp. 891–901.Google Scholar