Answer to Question #93058 in Discrete Mathematics for jose

Question

Go¨del′s completeness theorem asserts that ---

The first order proof system with Peano's axioms proves every statement true in the standard model

Peano's axioms form a consistent set of formulae

The first order proof system can prove all logical consequences of the proper axioms

The first order proof system proves only logical consequences of the proper axioms

Answer 1

Gödel's completeness theorem asserts that the first order proof system can prove all logical consequences of the proper axioms.