## The New Encyclopaedia Britannica, Volume 11Encyclopaedia Britannica, 1983 - Encyclopedias and dictionaries |

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Page 42

Sometimes the word "

word "thesis" is also used for this ... new wff's (

performing certain specified operations on axioms or previously obtained

Sometimes the word "

**theorem**" is used to cover axioms as well as**theorems**; theword "thesis" is also used for this ... new wff's (

**theorems**) to be obtained byperforming certain specified operations on axioms or previously obtained

**theorems**.Page 1083

Gddel's original proof of the completeness

second proof above. Consideration may ... M.89 — are not satisfiable; i.e., their

negations are tautologies (

12 V ...

Gddel's original proof of the completeness

**theorem**is closely related to thesecond proof above. Consideration may ... M.89 — are not satisfiable; i.e., their

negations are tautologies (

**theorems**of the propositional calculus). Thus, — <M12 V ...

Page 1085

One application of the Lowenheim-Skolem

models and is categorical in some infinite cardinality a, then the theory is

complete; i.e., for every closed sentence in the language of the theory, either that

sentence ...

One application of the Lowenheim-Skolem

**theorem**is: If a theory has no finitemodels and is categorical in some infinite cardinality a, then the theory is

complete; i.e., for every closed sentence in the language of the theory, either that

sentence ...

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