Meaning of these Closure Abbreviations

Question

What do these closure abbreviations stand for in Mathematical Logic?

Semantic Closure: Con($\Gamma$)

Syntactic Closure: Ded($\Gamma$)

...where $\Gamma$ is a set of well-formed formulas.

Answer 1

$\text {Con}(\Gamma)$ is the set of all formulas that are logical Consequence of the set (of formulas) $\Gamma$.

$\text {Ded}(\Gamma)$ is the set of all formulas that are derivable from the set (of formulas) $\Gamma$, i.e. there is a Deduction of them by way of the proof system.