| 释义 |
Löwenheim–Skolem, n. Logic.|ˈlɜːvənhaɪm ˈskɔːləm, ˈskəʊləm|
[The names of Leopold Löwenheim (1878–1957), German mathematician, and Thoralf Albert Skolem (1887–1963), Norwegian mathematician, who formulated the theorem.]
Löwenheim–Skolem theorem, the theorem that any consistent set of sentences may be interpreted by some finite or countable model.
1952S. C. Kleene Introd. Metamath. xiv. 394 If a predicate letter formula F is satisfiable in some (non-empty) domain, then F is satisfiable in the domain of the natural numbers. (Löwenheim's theorem, 1915, also called the Löwenheim-Skolem theorem.) 1965B. Mates Elem. Logic viii. 141 The question thus arises whether one could find a consistent set of sentences that is satisfiable only by interpretations having non-denumerably infinite domains. In view of the Löwenheim–Skolem theorem, the answer is negative. 1967J. van Heijenoort From Frege to Gödel 582 His proof yields, besides completeness, the Löwenheim–Skolem theorem, which states that a satisfiable formula is {aleph}0-satisfiable. 1982W. S. Hatcher Logical Found. Math. i. 38 Finally, we state (without proof) a modern form of the famous Löwenheim–Skolem theorem. |