The upward Löwenheim–Skolem theorem states that if a first-order theory has an infinite model, it has models of arbitrarily large…
A surjection, or onto function, ensures every element in the target set is reached by at least one element from…
An onto function, also known as a surjective function, maps elements from one set to another, ensuring every element in…
A fundamental theorem in mathematical logic stating that any countable theory with an infinite model has models of all infinite…
An inner model is a substructure of a larger model of set theory. It's a fundamental concept for understanding the…
An injective function, also known as an injective or one-to-one function, maps distinct elements of its domain to distinct elements…
The image of a function represents the set of all possible output values derived from its input domain. It's a…
An equivalence relation is a fundamental concept in mathematics. It's a binary relation that is reflexive, symmetric, and transitive, establishing…
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…