model theory of fields
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2019 ◽  
Vol 372 (8) ◽  
pp. 5991-6016
Author(s):  
Özlem Beyarslan ◽  
Daniel Max Hoffmann ◽  
Moshe Kamensky ◽  
Piotr Kowalski

2018 ◽  
Vol 18 (01) ◽  
pp. 1850003 ◽  
Author(s):  
Daniel M. Hoffmann ◽  
Piotr Kowalski

We study algebraic and model-theoretic properties of existentially closed fields with an action of a fixed finite group. Such fields turn out to be pseudo-algebraically closed in a rather strong sense. We place this work in a more general context of the model theory of fields with a (finite) group scheme action.


2017 ◽  
pp. 1-37 ◽  
Author(s):  
David Marker ◽  
David Marker ◽  
Margit Messmer ◽  
Anand Pillay

2016 ◽  
Vol 81 (2) ◽  
pp. 493-509
Author(s):  
OMAR LEÓN SÁNCHEZ ◽  
RAHIM MOOSA

AbstractA model companion is shown to exist for the theory of partial differential fields of characteristic zero equipped with free operators that commute with the derivations. The free operators here are those introduced in [R. Moosa and T. Scanlon, Model theory of fields with free operators in characteristic zero, Journal of Mathematical Logic 14(2), 2014]. The proof relies on a new lifting lemma in differential algebra: a differential version of Hensel’s Lemma for local finite algebras over differentially closed fields.


2016 ◽  
Author(s):  
David Marker ◽  
Margit Messmer ◽  
Anand Pillay

2014 ◽  
Vol 14 (02) ◽  
pp. 1450009 ◽  
Author(s):  
Rahim Moosa ◽  
Thomas Scanlon

Generalizing and unifying the known theorems for difference and differential fields, it is shown that for every finite free algebra scheme 𝒟 over a field A of characteristic zero, the theory of 𝒟-fields has a model companion 𝒟-CF0 which is simple and satisfies the Zilber dichotomy for finite-dimensional minimal types.


Author(s):  
David Marker ◽  
Margit Messmer ◽  
Anand Pillay

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