Amalgamation of types in pseudo-algebraically closed fields and applications

Journal of Mathematical Logic 19 (2):1950006 (2019)
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Abstract

This paper studies unbounded pseudo-algebraically closed fields and shows an amalgamation result for types over algebraically closed sets. It discusses various applications, for instance that omega-free PAC fields have the property NSOP3. It also contains a description of imaginaries in PAC fields.

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10.1142/s0219061319500065

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Citations of this work

On the antichain tree property.JinHoo Ahn, Joonhee Kim & Junguk Lee - 2022 - Journal of Mathematical Logic 23 (2).
Quantifier elimination on some pseudo-algebraically closed valued fields.Jizhan Hong - 2023 - Annals of Pure and Applied Logic 174 (1):103170.
The Embedding Property for Sorted Profinite Groups.L. E. E. Junguk - 2023 - Journal of Symbolic Logic 88 (3):1005-1037.

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References found in this work

Simple theories.Byunghan Kim & Anand Pillay - 1997 - Annals of Pure and Applied Logic 88 (2-3):149-164.
Generic structures and simple theories.Z. Chatzidakis & A. Pillay - 1998 - Annals of Pure and Applied Logic 95 (1-3):71-92.
On model-theoretic tree properties.Artem Chernikov & Nicholas Ramsey - 2016 - Journal of Mathematical Logic 16 (2):1650009.
Laforte, G., see Downey, R.T. Arai, Z. Chatzidakis & A. Pillay - 1998 - Annals of Pure and Applied Logic 95 (1-3):287.
On the automorphism groups of finite covers.David M. Evans & Ehud Hrushovski - 1993 - Annals of Pure and Applied Logic 62 (2):83-112.

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