Sentence examples for proof of completeness from inspiring English sources

The proof of completeness with respect to strong models bears a close similarity to the proof of completeness using canonical models for the modal logic \(\mathsf{K}\).

As in the proof of completeness of A ( X ), we infer that (2.4) holds.

This allows a proof of completeness but not a solution of problem (B).

This however can not be regarded as formal proof of completeness of our framework.

Different proofs of completeness of ⊢ have been published since, e.g. Kozen and Parikh [1981].

For detailed proofs of completeness of variations of these axiomatic systems, as well as proofs of decidability, see Segerberg (1970); Rescher and Urquhart (1971); Burgess (1979); Burgess and Gurevich (1985); and Goldblatt (1987).

This completes the proof of the completeness of ( A, D ).

The modal completeness theorem by Segerberg was an important first step in Solovay's proof of arithmetical completeness of GL with respect to Peano Arithmetic.

Gödel's original proof of the completeness theorem is closely related to the second proof above.

There has been outlined above a proof of the completeness of elementary logic without including sentences asserting identity.

Thus this proof of the Completeness Theorem gives also the Löweheim-Skolem Theorem (see below).