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 is true in that case. An operand of a disjunction is called a disjunct. Related concepts in other fields are: Or is usually expressed with an infix operator: in mathematics and logic, ∨; in electronics, +; and in most programming languages, |, ||, or or. In Jan Łukasiewicz's prefix notation for logic, the operator is A, for Polish "alternatywa" (English: alternative). Logical disjunction is an operation on two logical values, typically the values of two propositions, that has a value of "false" if and only if both of its operands are false. More generally, a disjunction is a logical formula