Relationship With Completeness
Decidability should not be confused with completeness. For example, the theory of algebraically closed fields is decidable but incomplete, whereas the set of all true first-order statements about nonnegative integers in the language with + and × is complete but undecidable. Unfortunately, as a terminological ambiguity, the term "undecidable statement" is sometimes used as a synonym for independent statement.
Read more about this topic: Decidability (logic)
Famous quotes containing the words relationship with, relationship and/or completeness:
“We think of religion as the symbolic expression of our highest moral ideals; we think of magic as a crude aggregate of superstitions. Religious belief seems to become mere superstitious credulity if we admit any relationship with magic. On the other hand our anthropological and ethnographical material makes it extremely difficult to separate the two fields.”
—Ernst Cassirer (1874–1945)
“If one could be friendly with women, what a pleasure—the relationship so secret and private compared with relations with men. Why not write about it truthfully?”
—Virginia Woolf (1882–1941)
“Poetry presents indivisible wholes of human consciousness, modified and ordered by the stringent requirements of form. Prose, aiming at a definite and concrete goal, generally suppresses everything inessential to its purpose; poetry, existing only to exhibit itself as an aesthetic object, aims only at completeness and perfection of form.”
—Richard Harter Fogle, U.S. critic, educator. The Imagery of Keats and Shelley, ch. 1, University of North Carolina Press (1949)