Elementary Equivalence in Logic and Mathematics
Elementary equivalence signifies that two structures share all the same first-order sentences.…
Effectively Decidable Theory
An effectively decidable theory is a formal system where an algorithm can…
Downward Löwenheim–Skolem Theorem
The downward Löwenheim–Skolem theorem states that if a theory has an infinite…
Conservative Extension in Logic and Mathematics
A conservative extension adds new axioms or rules to a theory without…
Comprehension Schema in Set Theory and Logic
The comprehension schema is a fundamental principle in set theory and logic.…
Compactness Theorem
A fundamental theorem in mathematical logic asserting that if every finite subset…
Categorical Logic
Categorical logic, rooted in category theory, explores object categorization and the logical…