Ueber die Nicht-charakterisierbarkeit der Zahlenreihe mittels endlich oder abzaehlbar unendlich vieler Aussagen mit ausschliesslich Zahlenvariablen¶
Skolem, T. (1934). Ueber die Nicht-charakterisierbarkeit der Zahlenreihe mittels endlich oder abzaehlbar unendlich vieler Aussagen mit ausschliesslich Zahlenvariablen.
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- Nobody chose that weakness for any particular axiom; it is contributed entirely by the frame, and it is the reason the first-order theory admits models other than the intended one while the second-order formulation does not.
This sourceEstablishes that an axiomatization restricted to number variables admits models other than the intended one, so the restriction the schema's slot imposes is what costs the theory its categoricity.
- Nobody chose that weakness for any particular axiom; it is contributed entirely by the frame, and it is the reason the first-order theory admits models other than the intended one while the second-order formulation does not.
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Registry ID ref:2279ca69ef13 · see in the full table