Lexicon of Arguments

 

Berka I 340
Loewenheim/Hilbert/Ackermann: Loewenheim has shown that every expression that is universal for the countable domain has the same property for every other domain. In Loewenheim, however, the sentence appears in the dual version:
Every formula of the function calculus is either contradictory or can be satisfied within a countable infinite range of thought.
>Satisfaction, >Satisfiability, >Models, >Model theory, >Functional calculus, >Countability.
General Validity/Hilbert/Ackermann: examples of formulas which are valid in each domain are all formulas that can be proved from axioms of a system.
>Validity, >Universal validity.
Loewenheim/Hilbert/Ackermann: Loewenheim has made another remarkable proposition: in the treatment of the logical formulas one can restrict oneself to those in which only function symbols with a maximum of two vacancies occur⁽¹⁾. This corresponds to:
Schroeder: the general relative calculus can be traced back to the binary calculus⁽²⁾.
>Logical formulas.

1. L. Löwenheim: Über Möglichkeiten im Relativkalkül, Math. Annalen 76 (1915), pp. 447-470, p. 459.
2. D. Hilbert & W. Ackermann: Grundzüge der Theoretischen Logik, Berlin, 6. Aufl. Berlin/Göttingen/Heidelberg 1972, § 12.