Topos theory generalizes set theory using abstract frameworks. It defines mathematical structures across various contexts, offering a powerful lens for…
A relation R is strongly connected if for any two elements x and y, either x is related to y…
Soundness ensures that a logical system's derived theorems are always true under any interpretation. It's a fundamental property for reliable…
The Skolem paradox highlights a contradiction between intuition and the Skolem-Lowenheim theorem. It shows that countable models can exist for…
A fundamental theorem in first-order logic. It asserts that if a theory has an infinite model, it possesses models for…
Sequent calculus is a formal system representing logical deductions. It uses sequences of formulas before and after a turnstile, signifying…
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…
Robinson arithmetic is a simplified version of Peano arithmetic, omitting the induction axiom schema. It provides a weaker yet still…