In first order logic, validity of a formula is determined based on every possible interpretation. Intuitively this means a sentence is true if it holds in every model or interpretation of our theory. Since the 1960s the main method set theorists have had to build new models of set theory has been forcing. The method of forcing has been a powerful tool in showing that certain sentences hold in some models of ZFC but fail in others. This gives rise to a natural family of questions and results centered around the concept of generic absoluteness, or what exactly can we change by forcing and what is ``fixed''.

In the 1990s Hugh Woodin developed $\Omega$-logic as a useful and natural way of thinking about these results and strengthening first order logic, by considering not all models, but only those that arise via forcing. In this talk I will introduce the semantic and syntactic notions of $\Omega$-logic and some of their important, and surprising properties. We will go over some fundamental results from first order logic (soundness, completeness, compactness) and see how they translate, or fail to translate to $\Omega$-logic. Finally I will state the $\Omega$-conjecture and, time-permitting, comment on some of the bold claims it has been used to support.