"Zum Entscheidungsproblem Des Logischen Funktionenkalküls"

GÖDEL, Kurt (1906-1978). "Zum Entscheidungsproblem des logischen Funktionenkalküls." Offprint from: Monatsheften für Mathematik und Physik , vol. 40, part 2. Leipzig: Akademische Verlagsgesellschaft, 1933. A fine copy of this extremely rare offprint, in which Gödel makes a rare error . In this paper, Gödel proves the decidability for the class of formulas called [∃*∀2∃*, all , (0)]. These formulas may contain arbitrary relations amongst the variables, but no functions or constants, and no equality symbol. However, Gödel ends the paper with the final sentence: 'In conclusion, I would still like to remark that Theorem I can also be proved, by the same method, for formulas that contain the = sign.' This was believed for about 30 years, until Stål Aanderaa in the mid-1960s showed that Gödel's proof would not actually work if the formulas contained equality. In 1983, Warren D. Goldfarb proved that Gödel had been mistaken, and the satisfiability of formulas in the larger class was not decidable. Only one other copy of this offprint has been recorded at auction (Christie's, 12 June 2013, lot 138). Octavo (234 x 156mm). 11pp., 433-443. Original stapled wrappers, the front wrapper with printed statement of presentation from the author (slight fading to lower margin of front wrapper). Custom cloth portfolio.

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