I am stuck as to how one would show a proof system is sound and complete assuming that we are using only finite sets, $\Omega $. In other words, knowing that for any finite set of formulas $\Omega $ and any formula $\phi$, $Ω ⊢ φ ⟺ Ω⊨φ$, how would I be able to show soundness and completeness?
2026-04-07 17:38:47.1775583527
Can Soundness and Completeness be shown for finite sets?
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