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.
Loosely associated statements missing from the passage is a claim that any one statement supports another. In "A concise introduction to logic", Hurley demonstrates the concept with a quote by Lao-Tzu: While each clause in the quote may seem related to the others, each provides no reason to believe another. Loosely associated statements A loosely associated statement is a type of simple non-inferential passage wherein statements about a general subject are juxtaposed but make no inferential claim. As a rhetorical device, loosely associated statements may be intended by the speaker to infer a claim or conclusion, but because they lack a coherent logical