Forking in differentially closed fields of positive characteristic

27.11.2024 11:30 - 10:00

P. Kowalski (U Wrocław, PL)

I will discuss another mathematical mistake of mine. Let \(p\) be a prime number and DCF\(_p\) denote the model companion of the theory of differential fields of characteristic \(p\). Shelah showed that the theory DCF\(_p\) is stable. It is easy to see that if \(K\) is an underlying field of a model of DCF\(_p\), then \(K\) is separably closed and \([K:K^p]\) is infinite, so \(K\) is a model of the theory SCF\(_{p,\infty}\). In "Derivations of the Frobenius map, Journal of Symbolic Logic, (1) 70 (2005), 99–110'', I claimed that the forking independence in DCF\(_p\) is given in some natural way by the forking independence in SCF\(_{p,\infty}\). However, Omar León Sánchez and Amador Martin-Pizarro recently kindly provided a counterexample for this claim.

Organiser:

KGRC

Location:

SR 10, 1. Stock, Koling. 14-16, 1090 Wien