The recent history of model theory
نویسنده
چکیده
The history of Model Theory can be traced back to the work of Charles Sanders Peirce and Ernst Schröder, when semantics started playing a role in Logic. But the first outcome dates from 1915. It appears in the paper Über Möglichkeiten im Relativkalkül (Math. Ann. 76, 445-470) by Leopold Löwenheim. The period from 1915 to 1935 is, in words of R.L. Vaught, extraordinary. The method of elimination of quantifiers is developed and applied to give decision methods for the theories of (Q, <) (C.H. Langford), of (ω,+) and (Z,+, <) (M. Presburger) and, finally, of the field of complex numbers and of the ordered field of real numbers (A. Tarski). Also the completeness theorem of Kurt Gödel (1930) has to be considered among the earliest results of Model Theory.
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