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  • 4.1: Introduction to Incompleteness
    https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Book%3A_Friendly_Introduction_to_Mathematical_Logic_(Leary_and_Kristiansen)/04%3A_Incompleteness_From_Two_Points_of_View/4.01%3A_Introduction_to_Incompleteness
    For the collection of logical axioms and rules of inference that we have set out, any formula ϕ that can be deduced from a set of nonlogical axioms Σ will be true in all models of \(\S...For the collection of logical axioms and rules of inference that we have set out, any formula ϕ that can be deduced from a set of nonlogical axioms Σ will be true in all models of Σ under any variable assignment function (that's soundness), and furthermore any formula ϕ that is true in all models of Σ under every assignment function will be deducible from Σ (that's completeness).

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