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Single Idea 17813

[filed under theme 5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems ]

Full Idea

The Löwenheim-Skolem theorem tells us that any theory with a true interpretation has a model in the natural numbers.

Gist of Idea

Löwenheim-Skolem says any theory with a true interpretation has a model in the natural numbers

Source

Nicholas P. White (What Numbers Are [1974], V)

Book Ref

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.96

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The 2 ideas from Nicholas P. White

17812

Finite cardinalities don't need numbers as objects; numerical quantifiers will do [White,NP]

17813

Löwenheim-Skolem says any theory with a true interpretation has a model in the natural numbers [White,NP]