[Serious] Could an omnipotent and omniscient god prove that he was God?

[Objectivist]

I follow the objective theory of knowledge, one in which knowledge is not aquired apriori but is acquired by mans of perceiving reality and identifying what is perceived by an objective means.  In other words, logic applied to observed facts.  There is no reason, in reason, to split truth in the way the analytic-synthetic does. 

How did you acquire the knowledge of the logic that you apply to observed facts?

By reason.  Reason is the how of knowledge.  Reason is the faculty that identifies and integrates perceptual data.   The fundamental law of logic is the law of identity which is axiomatic and therefore formed directly from perception.    Knowledge is a process of identification which is a process of integration and differentiation.  It starts with perception and then abstraction based directly from perceptual inputs and proceeds through abstraction from abstraction to form wider concepts such as the concept furniture from the concepts table, chair, bed , dresser, end table, etc.  Axiomatic concepts have a special place in the hierarchy of knowledge.  They are at the junction of the perceptual and conceptual level of consciousness.  

The law of identity is the recognition that to exist is to be something, to possess a specific identity or set of attributes.  Attributes are how we integrate and differentiate existents.  That's why a proper definition includes both a genus, the wider grouping an entity belongs to, and a differentia or the attribute which separates that group of concretes froom the rest of the genus.  For example, household items would be the genus and table would be a species within that genus.  In the definition of man, rational animal, the animal part is the genus and the rational part is the differentia.