I am relatively new to the formalism of Mathematical Logic, and don't know how denote the set of the wff logically deducible by a given set of premises $\Sigma$ in a predicate calculus $K.$ I have thought of $\textrm{Theor}(\Sigma),$ as an abbreviation for "theorems of $\Sigma$," but I don't know if it is acceptable.
Motivation: I needed such a notation, because $\Sigma$ is consistent (resp.consistent and complete) iff $\textrm{Theor}(\Sigma)/\tilde{}$ is a proper filter (ultrafilter) in $K^{\star},$ the Lindenbaum algebra of $K.$ In such a way the Lindenbaum's Lemma can be proved just invoking the Ultrafilter Lemma.
So my question is:
There is a standard notation for the set $\{\phi\mid\Sigma\vdash_K\phi\},$ where $K$ is first order predicate calculus and $\Sigma$ is a set of wff in $K$?
I would like to have references to actual usage. Thanks.