cardinality

Upward Löwenheim–Skolem Theorem

The upward Löwenheim–Skolem theorem states that if a first-order theory has an infinite model, it has models of arbitrarily large…

4 days ago

Skolem-Lowenheim Theorem

A fundamental theorem in first-order logic. It asserts that if a theory has an infinite model, it possesses models for…

4 days ago

Löwenheim–Skolem Theorem

A fundamental theorem in mathematical logic stating that any countable theory with an infinite model has models of all infinite…

4 days ago

Hume’s Principle

Hume's principle states that two collections have the same number of objects if and only if a one-to-one correspondence can…

4 days ago

Downward Löwenheim–Skolem Theorem

The downward Löwenheim–Skolem theorem states that if a theory has an infinite model, it has a model of every infinite…

4 days ago

Denumerable Sets: Understanding Countable Infinity

A denumerable set is one whose elements can be matched one-to-one with the natural numbers. This concept is fundamental to…

4 days ago

Cardinal Numbers

Cardinal numbers represent the quantity or size of a set. They answer the question 'how many?' and form the basis…

6 days ago