A cornerstone of computable function theory, the S-M-N theorem offers a way to create specific computable functions from general ones,…
Reverse mathematics investigates the logical strength of mathematical theorems. It aims to identify the minimal axiomatic systems required to prove…
A computation is register computable if it can be performed by a register machine. This concept is fundamental in theoretical…
Recursive function theory explores the properties of recursive functions, focusing on their computability and classification within complexity hierarchies. It's fundamental…
The recursion theorem, fundamental in computability theory, allows a function to call itself. It has significant implications in computer science,…
A primitive recursive relation is a type of relation definable using primitive recursive functions. These relations represent a subset of…
Primitive recursive functions are a subset of computable functions defined using initial functions and operations like composition and primitive recursion.…
Primitive recursion defines functions by calling themselves with simpler inputs. It requires a base case to ensure termination, forming a…
A theory is Post consistent if it contains at least one unprovable statement. If all statements are provable, the theory…
Markov's Principle, a cornerstone of constructive mathematics, asserts that if a property is impossible to lack, then an object possessing…