Easy Proofs of Löwenheim-Skolem Theorems by Means of Evaluation Games

Abstract

We propose a proof of the downward Löwenheim-Skolem that relies on strategies deriving from evaluation games instead of the Skolem normal forms. This proof is simpler, and easily understood by the students, although it requires, when defining the semantics of first-order logic to introduce first a few notions inherited from game theory such as the one of an evaluation game.

arXiv commentProceedings of the Fourth International Conference on Tools for Teaching Logic (TTL2015), Rennes, France, June 9-12, 2015. Editors: M. Antonia Huertas, João Marcos, María Manzano, Sophie Pinchinat, François Schwarzentruber