A technique in mathematical logic to remove quantifiers from formulas, preserving logical equivalence. Crucial in theories like real closed fields…
Elementary equivalence signifies that two structures share all the same first-order sentences. This concept is crucial in model theory for…
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 effectively computable function is one that can be calculated by an algorithm. This means a step-by-step procedure exists, guaranteeing…
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…
The principle of double negation introduction states that for any proposition P, P implies the double negation of P (¬¬P).…
Double negation elimination is a core principle in classical logic. It states that a statement preceded by two negations is…
Double negation is the logical principle where applying negation twice to a statement returns the original statement. In classical logic,…