Skolem-Lowenheim Theorem
A fundamental theorem in first-order logic. It asserts that if a theory…
Single Turnstile Symbol in Logic
The single turnstile (⊢) symbol in logic signifies syntactic entailment. It indicates…
Understanding Signatures in Logic and Algebra
A signature in logic and algebra defines the set of symbols and…
Understanding Seriality in Relations and Logic
Seriality defines a property of relations, ensuring every element in the domain…
Sequence: Definition and Mathematical Concepts
A sequence is an ordered list of objects, identified by position. It's…
Sentential Logic
Sentential logic, also known as propositional logic, examines the relationships between complete…
Semi-Decidable Theory
A semi-decidable theory allows for an algorithm to list all its theorems.…
Second-Order Logic Explained
Second-order logic enhances first-order logic by enabling quantification over predicates and relations,…
Satisfaction in Model Theory
Satisfaction in model theory describes the relationship between a structure and a…
Rule of Replacement in Formal Logic
A fundamental principle in formal logic that permits substituting logically equivalent expressions…