High Quality Content by WIKIPEDIA articles! For example, a theory T of arithmetic is said to be inconsistent if there exists a proof in T of the formula "0=1". The formula I(T), which says that T is inconsistent, is thus an existential formula. A witness for the inconsistency of T is a particular proof of "0 = 1" in T. Boolos, Burgess, and Jeffrey (2002:81) define the notion of a witness with the example, in which S is an n-place relation on natural numbers, R is an n-place recursive relation, and ? indicates logical equivalence (if and only if):" S(x1, ..., xn) ? ?y R(x1, . . ., xn, y) " A y such that R holds of the xi may be called a 'witness' to the relation S holding of the xi (provided we understand that when the witness is a number rather than a person, a witness only testifies to what is true)." In this particular example, B-B-J have defined s to be (positively) recursively semidecidable, or simply semirecursive.

Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.