Model completeness.
A sentence X in the lower predicate calculus L is said to be defined in a set K of sentences in L if all the extralogical symbols of X occur in K. K is said to be complete if every sentence X in L which is defined in K and which is consistent with K, is deducible from K. Semantically, the completene...
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| Format: | Others |
| Language: | en |
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McGill University
1961
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| Online Access: | http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=113424 |
| Summary: | A sentence X in the lower predicate calculus L is said to be defined in a set K of sentences in L if all the extralogical symbols of X occur in K. K is said to be complete if every sentence X in L which is defined in K and which is consistent with K, is deducible from K. Semantically, the completeness of a set K asserts that any two models of K satisfy the same "axioms" (sentences) which can be formulated in L using only the extralogical symbols that appear in K. Thus from the fact that the set K* of axioms for the concept of an algebraically closed field of specified characteristic is complete, it follows that a sentence X in L which is satisfied by the field of complex numbers is satisfied also by all fields of characteristic zero. |
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