 Complete omega-consistent arithmetic theories are sound

A bounded-complete complete omega-consistent arithmetic first-order theory is correct on every arithmetic first-order sentence. Completeness and first-order consistency make its theoremhood obey the Boolean truth tables. Omega-consistency ensures that every proved existential sentence has a provable standard numeral instance, since otherwise completeness refutes all such instances. Induction on logical formulas now identifies theoremhood with standard truth.