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Ideas for 'fragments/reports', 'On Euclidean Geometry' and 'Remarks on axiomatised set theory'

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5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems

17878

If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem]

5. Theory of Logic / K. Features of Logics / 1. Axiomatisation

16886

The truth of an axiom must be independently recognisable [Frege]