The upward Löwenheim–Skolem theorem states that if a first-order theory has an infinite model, it has models of arbitrarily large…
A semi-decidable theory allows for an algorithm to list all its theorems. However, it may not offer a way to…
Recursive function theory explores the properties of recursive functions, focusing on their computability and classification within complexity hierarchies. It's fundamental…
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…
A Henkin sentence is a self-referential statement that asserts its own provability within a formal system. It's a foundational concept…
A self-referential sentence in formal systems, a Gödel sentence demonstrates incompleteness theorems by asserting its own unprovability within that system.…
The downward Löwenheim–Skolem theorem states that if a theory has an infinite model, it has a model of every infinite…
A crucial lemma in Gödel's incompleteness theorems. It states that for any formula with one free variable, there exists a…
Church's theorem proves the undecidability of fundamental decision problems in logic, like the Entscheidungsproblem. It demonstrates that no logic can…