A sequence of numbers where each element is chosen without any predetermined rule or algorithm. It's a concept central to…
First-order logic (FOL) is a formal system using quantifiers like 'for all' and 'there exists' to reason about individuals. It's…
Finite model theory explores structures with finite domains. It investigates properties and expressiveness of logical languages within these finite settings,…
Expressive completeness, also known as functional completeness, refers to a programming language's ability to express any computable function. It's a…
A rule of inference in logic that allows the introduction of an existential quantifier (∃). It asserts the existence of…
Existential instantiation is a logical rule enabling the inference of a specific individual's existence from a generic existential statement. It's…
Existential generalization is a rule of inference that permits concluding that something exists with a specific property. This conclusion is…
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 effective procedure is a guaranteed method for solving problems in a finite, repeatable sequence of steps. It ensures a…