I need to classify the set $$\{p|∃y : \operatorname{Dom}(φ p ) ⊇ \operatorname{Dom}(φ y )\}$$ as decidable, semidecidable or not semidecidable.
I don't know how to start. Any ideas?
Dom (φp) it's all the inputs that are accepted by a turing machine "p", and the same for Dom (φy). So if My(some input) accepts then Mp(same input) accepts too, Mp can accept more inputs than My but not less.
But I don't know how work with that.