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|Berka I 489
Accuracy/range/Tarski: according to the sentences 14-16 (or Lemma I) there is for each natural number k such a statement that is true in any area with k elements and in any area of the other thickness - in contrast: every in an infinite range true statement is also true in any other infinite domain (without regard to the thickness) - properties/classes: so we conclude that the object language allows us to express such a property of classes of individuals, such as the existence of exactly k elements - there is no means against rewarding any specific type of infinity (e.g. countability) and we cannot by means of a single or a finite number of statements.
Two such properties of classes such as finiteness, infinity to distinguish them from each other - (Tarski:> Löwenheim).
Truth (in the domain): depends on the scope in the finite case, not in the infinite.
Berka I 491
Accuracy in the doamin/Provability/Tarski: if we add the statement a (every nonempty class contains a singleton class as a part) to AxS Correctness/provability will be coextensive terms - N.B.: this does not work in the logical algebra, because here a is not satisfied in all interpretations.
"In every correct domain"/Tarski: this term stands according to the extent in the middle between the provable sentence and the true statement - but is narrower than the class of all true statements generally - it does not contain statements whose validity depends on how big is the total number of individuals.
Logic, Semantics, Metamathematics: Papers from 1923-38 Indianapolis 1983
K. Berka/L. Kreiser
Logik Texte Berlin 1983