There is a big difference between the kinds of formulas seen in traditional term logic and the predicate calculus that is the fundamental advance of modern logic.
32.
The second notion was derived from work in predicate calculus ( predicate logic, first order logic ) and is prominent in modern theories of syntax and grammar.
33.
After the basic form of the theorem is proved, it will be easy to extend it to the case of predicate calculus " with equality ".
34.
For example a language in the first-order predicate calculus might include one of more predicate symbols and one or more individual constants and one or more variables.
35.
If you're not familiar with first-order predicate calculus, you're likely to find any serious graduate set theory text to be absolutely impenetrable.
36.
We axiomatize predicate calculus " without equality ", i . e . there are no special axioms expressing the properties of equality as a special relation symbol.
37.
The formal system described above is sometimes called the "'pure "'monadic predicate calculus, where " pure " signifies the absence of function letters.
38.
It resembles predicate calculus, and has affinities with Categorial Grammar, but these are findings after the fact which did not guide its development or the research that led to it.
39.
The Calculus of Constructions extends this isomorphism to proofs in the full intuitionistic predicate calculus, which includes proofs of quantified statements ( which we will also call " propositions " ).
40.
Generalizations include those for classifying foliations, and the classifying toposes for logical theories of the predicate calculus in intuitionistic logic that take the place of a'space of models '.
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