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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.
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.
Löwenheim/Hilbert/Ackermann: Löwenheim 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.(2) This corresponds to:
Schröder: the general relative calculus can be traced back to the binary calculus.(1)
1. D. Hilbert und W. Ackermann, Grundzüge der theoretischen Logik, Berlin (6. Aufl. Berlin/Göttingen/Heidelberg 1972), § 12.
2. L. Löwenheim, Über Möglichkeiten im Relativkalkül, Math. Annalen 76 (1915), S. 447-470, S. 459_____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. The note [Author1]Vs[Author2] or [Author]Vs[term] is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.
Logik Texte Berlin 1983