We establish versions of Szegő’s distance formula and Widom’s theorem on invertibility (a family of) Toeplitz operators in a class finite codimension subalgebras uniform algebras, obtained by imposing number linear constraints. Each such algebra is naturally represented reproducing kernel Hilbert spaces, which play central role the proofs.

In the present paper, by considering the notion of ideals in $MV$-algebras, we study some kinds of ideals in $MV$-algebras and obtain some results on them. For example, we present definition of ultra ideal in $MV$-algebras, and we get some results on it. In fact, by definition of ultra ideals, we present new conditions to have prime ideals, positive implicative ideals and maximal ideals in $MV$...

We prove that if μ+ < λ = cf(λ) < μא0 for some regular μ > 2א0 , then there is no family of less than μא0 c-algebras of size λ which are jointly universal for c-algebras of size λ. On the other hand, it is consistent to have a cardinal λ ≥ א1 as large as desired and satisfying λ<λ = λ and 2λ + > λ++, while there are λ++ c-algebras of size λ+ that are jointly universal for calgebras of size λ+. ...

The syntactic monoid of a language is generalized to the level of a symmetric monoidal closed category D. This allows for a uniform treatment of several notions of syntactic algebras known in the literature, including the syntactic monoids of Rabin and Scott (D “ sets), the syntactic semirings of Polák (D “ semilattices), and the syntactic associative algebras of Reutenauer (D = vector spaces)....