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|Numbers||Berka I 539
Ordinals / ordinal numbers /o.n./ Tarski: we need them to classify characters of infinite order - it is a generalization of the concept of natural numbers - these are the smallest o.n. -
transfinite o.n.: since there are figures for every infinite sequence of o.n that are larger than any member of the sequence, there are particular numbers that are greater than all natural numbers - in every non-empty class of o.n. there is a smallest number - Omega / Omega / w: in particular there is the smallest transfinite o.n. w (Omega). the next largest is w + 1 and so on - the language of the general set theory is of order w.
Logic, Semantics, Metamathematics: Papers from 1923-38 Indianapolis 1983
K. Berka/L. Kreiser
Logik Texte Berlin 1983