The paper investigates the extension of a many-valued logic with fixed points. The logic under consideration is Ł$Π$, the most expressive known logic based on a continuous t-norm. The author uses novel methods: the existence of a proper semantics being hinged on the Brouwer Theorem rather than the usual Tarski Theorem. The main results of the paper include “standard completeness” for the introduced logic ($μ$Ł$Π$) and a categorical equivalence between its linearly ordered algebraic semantics and real closed fields. This equivalence is also extended to the full algebraic semantics of $μ$Ł$Π$ and a class of structures which suitably generalise real closed fields to non-linearly ordered structures.
Reviewer: Agata Ciabattoni (Wien)