He puts on airs and claims himself to be omniscient.

Omniscient : knowing everything.
Ignorant : lacking knowledge or awareness in general; uneducated or unsophisticated.
Uneducated : having or showing a poor level of education.
Unqualified : (of a person) not officially recognized as a practitioner of a particular profession or activity through having satisfied the relevant conditions or requirements.
Backward : directed behind or to the rear.

Antonym of Omniscient is Ignorant