First-Order Variables in Logic
First-order variables are placeholders for individuals within a specific domain in first-order…
First-Order Theory
A first-order theory formalizes mathematical reasoning using first-order logic. It defines relationships…
Finite Model Theory
Finite model theory explores structures with finite domains. It investigates properties and…
Elementary Equivalence in Logic and Mathematics
Elementary equivalence signifies that two structures share all the same first-order sentences.…
Downward Löwenheim–Skolem Theorem
The downward Löwenheim–Skolem theorem states that if a theory has an infinite…
Compactness Theorem
A fundamental theorem in mathematical logic asserting that if every finite subset…