As a current atheist, who was a former theist, I feel that God is not a logically incoherent concept. However, many definitions of God, especially those that involve omnipotence, omniscience etc. are very difficult to do without logical contradictions. I am interested in definitions for these concepts that work as follows:
Define a binary relation as follows: Given two agents X and Y, X <= Y if and only if Y can do all the things X can do. An omnipotent agent is a greatest upper bound on the set of agents, under the above relation.
As it stands this definition itself still has paradoxes, but I wonder if someone has been able to take a definition like this, perhaps in a category theoretic context (instead of a mere poset) and use it to formalise concepts like omniscience, omnipotence etc. without contradictions?