Finitary methods involve processes or operations that conclude after a limited number of steps or elements. This concept is fundamental…
Hilbert's Entscheidungsproblem sought an algorithm to determine the truth of any mathematical statement. Alan Turing and Alonzo Church proved it…
An effectively decidable theory is a formal system where an algorithm can definitively prove any statement as either true or…
An effectively decidable relation is one where a mechanical method can definitively determine if a pair of elements satisfies the…
An effective procedure is a guaranteed method for solving problems in a finite, repeatable sequence of steps. It ensures a…
The downward Löwenheim–Skolem theorem states that if a theory has an infinite model, it has a model of every infinite…
A deterministic Turing machine (DTM) is a theoretical model of computation. For every state and input symbol, it has exactly…
A decision procedure is a systematic algorithm that determines if statements are theorems or non-theorems within a logical system. It…
A theory with a decision procedure, allowing algorithmic determination of truth or falsehood for any statement within its framework. This…
A fundamental procedure in proof theory that systematically removes 'cuts' from a proof. This process simplifies proofs and demonstrates that…