Category
page 1Metatheorems
Gödel's incompleteness theorems
theorem that a wide class of logical systems cannot be both consistent and complete
Entscheidungsproblem
In mathematics and computer science, the ; ) is a challenge posed by David Hilbert and Wilhelm Ackermann in 1928. It asks for an algorithm that considers an inputted statement and answers "yes" or "no" according to whether it is universally valid, i.e., valid in every structure. Such an algorithm was proven to be impossible by Alonzo Church and Alan Turing in 1936.
Löwenheim–Skolem theorem
theorem that, for any signature 𝜎, any infinite 𝜎-structure 𝑀 and any infinite cardinal 𝜅≥|𝜎|, there is a 𝜎‐structure 𝑁 of cardinality 𝜅 that is either an elementary substructure or an elementary extension of 𝑀
Gödel's completeness theorem
fundamental theorem in mathematical logic
compactness theorem
theorem
deduction theorem
theorem
Tarski's undefinability theorem
theorem that truth in the standard model of a formal system cannot be defined within the system
Herbrand's theorem
reduction of first-order mathematical logic to propositional logic
Löb's theorem
theorem
metatheorem
In logic, a metatheorem is a statement about a formal system proven in a metalanguage. Unlike theorems proved within a given formal system, a metatheorem is proved within a metatheory, and may reference concepts that are present in the metatheory but not the object theory.
Frege's theorem
metatheorem that states that the Peano axioms of arithmetic can be derived in second-order logic from Hume's principle
Lindström's theorem
Theorem in mathematical logic
Courcelle's theorem
on linear-time algorithms for graph logic