Lexicon of Arguments

 Philosophical and Scientific Issues in Dispute
 
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Berka I 539
Ordinals/ordinal numbers/Tarski: we need them to classify characters of infinite order. - It is a generalization of the concept of natural numbers. - These are the smallest ordinal number.
Transfinite ordinal numbers: since there are figures for every infinite sequence of ordinal numbers 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 ordinal numbers there is a smallest number.
Omega/ω: in particular there is the smallest transfinite ordinal number ω (Omega).
The next largest is ω + 1 and so on. - The language of the general set theory is of order ω.(1)
>Numbers, >Set theory.


1. A.Tarski, Der Wahrheitsbegriff in den formalisierten Sprachen, Commentarii Societatis philosophicae Polonorum. Vol 1, Lemberg 1935

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