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 disjunction Logical disjunction In logic and mathematics, or is the truth-functional operator of (inclusive) disjunction, also known as alternation; the "or" of a set of operands is true if and only if "one or more" of its operands is true. The logical connective that represents this operator is typically written as ∨ or +. formula_1 is true if formula_2 is true, or if formula_3 is true, or if both formula_2 and formula_3 are true. In logic, "or" by itself means the "inclusive" "or", distinguished from an exclusive or, which is false when both of its arguments are true, while an "or"