Ideas from 'What Numbers Are' by Nicholas P. White [1974], by Theme Structure

[found in 'Philosophy of Mathematics: anthology' (ed/tr Jacquette,Dale) [Blackwell 2002,0-631-21870-x]].

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5. Theory of Logic / J. Model Theory in Logic / 3. L÷wenheim-Skolem Theorems
L÷wenheim-Skolem says any theory with a true interpretation has a model in the natural numbers
6. Mathematics / A. Nature of Mathematics / 3. Numbers / p. Counting
Finite cardinalities don't need numbers as objects; numerical quantifiers will do