Answer by rzach for Can the Completeness Theorem be proven constructively in...
What I had in mind was simply that some proof systems lend themselves to systematic proof search which, if $\models A$, is guaranteed to be successful. E.g., in sequent calculus LK, you basically apply...
View ArticleAnswer by Mark Saving for Can the Completeness Theorem be proven...
First, it is easy to show that natural deduction systems prove exactly the same sentences as Hilbert systems. This is a purely syntactic fact and can be proved constructively. It is therefore...
View ArticleCan the Completeness Theorem be proven constructively in a natural-deductive...
In Sets, Logic and Computation the following is said of the Completeness Theorem:When completeness is thought of as “whenever $\models A$ then $\vdash A$,” it may be hard to even come up with an idea:...
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