The upward Löwenheim–Skolem theorem states that if a first-order theory has an infinite model, it has models of arbitrarily large…
A fundamental theorem in first-order logic. It asserts that if a theory has an infinite model, it possesses models for…
A fundamental theorem in mathematical logic stating that any countable theory with an infinite model has models of all infinite…
Hume's principle states that two collections have the same number of objects if and only if a one-to-one correspondence can…
The downward Löwenheim–Skolem theorem states that if a theory has an infinite model, it has a model of every infinite…
A denumerable set is one whose elements can be matched one-to-one with the natural numbers. This concept is fundamental to…
Cardinal numbers represent the quantity or size of a set. They answer the question 'how many?' and form the basis…