Perhaps you might want to explain what you mean by limited. If one is the origin of Logic and Logic is God's thinking, how is that limited?
Being limited by logic means being bound by the rules of logic. As I recall, you said this is the case with God.
God is logic, His thinking is logic. How is God as the origin of logic limited by it? He thinks according to His logical thought.
So... God thinks according to his logical thought. Can his thoughts be illogical? Your position appears to be no. Therefore his thoughts are limited by logic.
Explain how omniscient thought is not cohesive with origins of mathematics and logic.
I already did. Gödel proved that any non-trivial self-consistent logical system must contain propositions which are true or false but cannot be shown to be either, and consequently cannot be known to be true or false either.
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