A hypothetical super-intelligent being used in philosophical problems. Omega is most commonly used as the predictor in Newcomb's problem. Sometimes Omega is taken as a perfect predictor, while other times it is an almost perfect predictor. In some thought experiments, Omega is also taken to be super-powerful.
Omega can be seen as analogous to Laplace's demon, or as the closest approximation to the Demon capable of existing in our universe.
In the case where Omega is considered a perfect predictor, it can become unclear what exactly omega is predicting. Take for example Parfit's Hitchhiker. In this problem, you are trapped dying in a desert and a passing driver will only pick you up if you promise to pay them $100 once you are in town. If the driver is a perfect predictor, then someone who always defects will never end up in town, so it is unclear what exactly they are predicting, since the situation is contradictory and the Principle of Explosion means that you can prove anything.
Counterfactuals for Perfect Predictors suggests that even if we can't predict what an agent would do in an inconsistent situation, we can predict how it would respond if given input representing an inconsistent situation (we can represent this response as an output). And indeed Updateless Decision Theory uses input-output maps so it doesn't run into this issue.