A fundamental theorem in first-order logic. It asserts that if a theory has an infinite model, it possesses models for…
The single turnstile (⊢) symbol in logic signifies syntactic entailment. It indicates that a formula or set of formulas can…
A signature in logic and algebra defines the set of symbols and their arities, specifying the operations, functions, and relations…
Seriality defines a property of relations, ensuring every element in the domain maps to at least one element in the…
A sequence is an ordered list of objects, identified by position. It's fundamental in mathematics for defining functions, sets, and…
Sentential logic, also known as propositional logic, examines the relationships between complete sentences or propositions. It focuses on how these…
A semi-decidable theory allows for an algorithm to list all its theorems. However, it may not offer a way to…
Second-order logic enhances first-order logic by enabling quantification over predicates and relations, not just individuals. It offers greater expressive power…
Satisfaction in model theory describes the relationship between a structure and a sentence, where the structure makes the sentence true…
A fundamental principle in formal logic that permits substituting logically equivalent expressions within proofs. This ensures the argument's validity is…