The Soundness Theorem states that if a statement can be derived from a set of axioms using a formal proof system, then that statement is true in every model of the axioms. This concept connects directly to the consistency and independence of axioms, as it ensures that any provable statement reflects the truth within the structure defined by those axioms. Soundness provides a foundational guarantee that logical deductions preserve truth, which is essential for understanding the reliability of formal systems.
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