Logisch-kombinatorische Untersuchungen über die Erfüllbarkeit oder Bewesibarkeit mathematischer Sätze nebst einem Theoreme über dichte Mengen. Offprint

Skolem, Thoralf (1887-1963). Logisch-kombinatorische Untersuchungen über der Erfüllbarkeit und Beweisbarkeit mathematischen Sätze nebst einem Theoreme über dichte Mengen. Offprint from Skrifter utgit av Videnskabsselskapet i Kristiania, I. Matematisk-naturvidenskabelig klasse, 4 (1920). 36pp. 274 x 182 mm. Later wrappers, but very good. First Edition, Offprint Issue. "Many logicians would agree that Skolem and Gödel are the two greatest logicians of the [20th] century" (Wang, p. 119). In the present paper, Skolem "proved the theorem which is now known as the Löwenheim-Skolem theorem. Briefly, this states that if a finite or countable infinite set of sentences formalized within a first order predicate calculus is satisfiable (or, in other terminology, has a model), then the sentences are satisfiable within a countable domain" (Fenstad, p. 102). Another way of phrasing the theorem would be to state that if a theory has a model, then it has a countable model. The Löwenheim-Skolem theorem is one of the foundations of automated theorem proving. "The key work for automated deduction was that of Skolem. He carried out a systematic study of the problem of the existence of an interpretation which will satisfy a given formula of the predicate calculus, or, as one says, whether the given formula is satisfiable" (Davis, p. 9). Skolem was an exception to the rule that mathematicians do their best work when young—his first important paper dates from 1919, when he was thirty-two years old, and he continued to publish significant work until the end of his life. The papers that he published from 1920 on "gave him instant recognition as one of the foremost among logicians" (Fenstad, p. 101). M. Davis, "The prehistory and early history of automated deduction," Automation of Reasoning: Classical Papers on Computational Logic (1983): 1-28. J. Fenstad, "Thoralf Albert Skolem 1887-1963: A brief biographical sketch," Nordic Journal of Philosophical Logic 1 (1996): 99–106. Heijenoort, From Frege to Gödel, pp. 252-263 (reprinting Skolem’s paper). Origins of Cyberspace 365. Wang, "Skolem and Gödel," Nordic Journal of Philosophical Logic 1 (1996): 119-132. .