Semantic consequence describes the logical relationship between premises and a conclusion in a formal language. It guarantees that no interpretation…
Reflexivity means every element in a set is related to itself. This fundamental property is crucial in understanding various mathematical…
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,…
Primitive recursive functions are a subset of computable functions defined using initial functions and operations like composition and primitive recursion.…
An onto function, also known as a surjective function, maps elements from one set to another, ensuring every element in…
Quine's New Foundations is a set theory designed to bypass paradoxes of naive set theory. It uses a unique axiom…
The set of positive integers, often denoted by N, typically including zero. Natural numbers form the foundation for counting, ordering,…
A maximal consistent set is a collection of logical formulas that is both consistent and cannot be extended further without…
A linear order, also known as a total order, is a fundamental concept in mathematics. It's a way to arrange…