display all the ideas for this combination of texts
2 ideas
10761 | Completeness can always be achieved by cunning model-design [Rossberg] |
Full Idea: All that should be required to get a semantics relative to which a given deductive system is complete is a sufficiently cunning model-theorist. | |
From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §5) |
10755 | A deductive system is only incomplete with respect to a formal semantics [Rossberg] |
Full Idea: No deductive system is semantically incomplete in and of itself; rather a deductive system is incomplete with respect to a specified formal semantics. | |
From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
A reaction: This important point indicates that a system might be complete with one semantics and incomplete with another. E.g. second-order logic can be made complete by employing a 'Henkin semantics'. |