Robinson arithmetic is a simplified version of Peano arithmetic, omitting the induction axiom schema. It provides a weaker yet still…
Reverse mathematics investigates the logical strength of mathematical theorems. It aims to identify the minimal axiomatic systems required to prove…
A relative consistency proof demonstrates that if a system S is consistent, adding new axioms to S also maintains consistency.…
Reflexivity means every element in a set is related to itself. This fundamental property is crucial in understanding various mathematical…
A recursive relation defines a relationship based on its own previous terms. This allows for the definition of sequences and…
Recursive function theory explores the properties of recursive functions, focusing on their computability and classification within complexity hierarchies. It's fundamental…
A recursive definition defines a mathematical object by referring to itself. It requires a base case to stop the recursion…
The range of a function encompasses all possible output values it can generate from its domain. It's a fundamental concept…
An extension of the simple theory of types, the ramified theory introduces levels to distinguish objects and functions by order,…
QED, a Latin phrase meaning "which was to be demonstrated," marks the conclusion of a mathematical proof or logical argument.…