Infinitary logic logical axiom, an element of T, or is deduced from previous statements using a rule of inference. As before, all rules of inference in finitary logic can be used, together with an additional one: The logical axiom schemata specific to infinitary logic are presented below. Global schemata variables: formula_3 and formula_18 such that formula_23. The last two axiom schemata require the axiom of choice because certain sets must be well orderable. The last axiom schema is strictly speaking unnecessary as Chang's distributivity laws imply it, however it is included as a natural way to allow natural weakenings to the logic.
Logical NOR Logical NOR In boolean logic, logical nor or joint denial is a truth-functional operator which produces a result that is the negation of logical or. That is, a sentence of the form ("p" NOR "q") is true precisely when neither "p" nor "q" is true—i.e. when both of "p" and "q" are "false". In grammar, nor is a coordinating conjunction. The NOR operator is also known as Peirce's arrow—Charles Sanders Peirce introduced the symbol ↓ for it, and demonstrated that the logical NOR is completely expressible: by combining uses of the logical NOR it is possible to express any logical