The Löwenheim-Skolem theorem for Gödel logic
Juan P. Aguilera · Annals of Pure and Applied Logic · 2023
We prove the following Löwenheim-Skolem theorems for first-order Gödel logic: For the Gödel logic G[0,1], a sentence ϕ has models of every infinite cardinality if and only if it has a model of cardinality ℶω(=sup{ℵ0,2ℵ0,…}). For an arbitrary Gödel logic GT, a sentence ϕ has models of every infinite cardinality if and only if it has a model of cardinality ℶω1.