Prime deductive systems and injective objects in the algebras of Łukasiewicz infinite-valued calculi
The author explores logical aspects of Wajsberg algebras. He proves that in any Wajsberg algebra, any proper implicative filter can be extended to a prime filter, and any proper deductive system can be extended to a maximal deductive system. He characterizes injective Wajsberg algebras as the retracts of powers of the algebra \(\mathbb{R}[0,1]\), and he proves that this characterization is equivalent to Sikorski Extension Theorem.
scientific article; zbMATH DE number 146929
scientific article