= Relative consistency
{title2=$\operatorname{Con}(T)\Rightarrow\operatorname{Con}(S)$}
A relative-consistency result constructs a <model of a first-order theory> $S$, or interprets its proofs, from the assumed consistency of a background theory $T$. It establishes $\operatorname{Con}(T)\Rightarrow\operatorname{Con}(S)$ in the stated metatheory, not an unconditional proof of consistency. For independence of an axiom $\varphi$ from $S$, obtain consistent models of both $S+\varphi$ and $S+\neg\varphi$, relative to the background assumption.
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