Logic MT24, Löwenheim-Skolem theorem
Flashcards
@Define what it means for a structure to be countable.
It has a countable domain.
@State the weak downwards Löwenheim-Skolem theorem.
Every consistent set of sentences has a countable model.
@Justify the weak downwards Löwenheim-Skolem theorem using the proof of Gödel’s Completeness Theorem, i.e. that every consistent set of sentences has a countable model.
The model used to show a consistent set of sentences is satisfiable was the Henkin model, which was countable.