Hume's principle states that two collections have the same number of objects if and only if a one-to-one correspondence can…
A homomorphism is a structure-preserving map between algebraic structures of the same type. It ensures that operations like addition and…
An ambitious project by David Hilbert to formalize all mathematics and prove its consistency using finitary methods. It aimed to…
Higher-order logic extends first-order logic by enabling quantification over predicates and other higher-order entities. It offers greater expressive power for…
A hierarchy ranks entities based on criteria, seen in organizational structures and set theory. Tarski's and cumulative hierarchies are key…
A hereditary property in mathematics and logic is a characteristic that, if held by an object, is also present in…
A Henkin sentence is a self-referential statement that asserts its own provability within a formal system. It's a foundational concept…
Gödel's second incompleteness theorem states that no consistent formal system strong enough to include basic arithmetic can prove its own…
Gödel's First Incompleteness Theorem states that any consistent formal system capable of basic arithmetic contains true statements that are unprovable…
A self-referential sentence in formal systems, a Gödel sentence demonstrates incompleteness theorems by asserting its own unprovability within that system.…