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math.LO2024
The class of Krasner hyperfields is not elementary
Piotr Błaszkiewicz, Piotr Kowalski
We show that the class of Krasner hyperfields is not elementary. To show this, we determine the rational rank of quotients of multiplicative groups in field extensions. Our argumen…
math.LO2023
Of model completeness and algebraic groups
Daniel Max Hoffmann, Piotr Kowalski, Chieu-Minh Tran +1
We show that if G is a split semisimple algebraic group over a model complete field K, then the groups G(K) and G(K)' (the commutator group which is a ``Chevalley group'' as for ex…