Negative resolution to the $C^{\ast }$-algebraic Tarski problem

Srivatsav Kunnawalkam Elayavalli, Christopher Schafhauser

We compute the $K_1$-group of ultraproducts of unital, simple $C^{\ast }$-algebras with unique trace and strict comparison. As an application, we prove that the reduced free group $C^{\ast }$-…