Answer by Kaveh for Adequacy theorem for propositional calculus
Moving from a (countable) consistent complete theory to a syntactic model can be done computably. However obtaining a consistent complete extension cannot be done computably (see Godel's first...
View ArticleAnswer by user642796 for Adequacy theorem for propositional calculus
One can provide a constructive proof of the propositional Adequacy Theorem, though it is (necessarily) much more involved. The classical one, due to Kalmar and contained in Mendelson's Introduction to...
View ArticleAnswer by Apostolos for Adequacy theorem for propositional calculus
In the very general case the a weaker form of the axiom of choice is needed, namely the Prime Ideal Theorem. This is because, in the general case, an ultrafilter in the Lindenbaum's algebra is a...
View ArticleAdequacy theorem for propositional calculus
I have been thinking about the following classical theorem of propositional calculus:Adequacy Theorem:if $A$ is a tautology then $A$ is provable by the logical axiomsNow "$A$ is a tautology" is a...
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