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…
The halting problem asks if it's possible to determine if any given program will halt or run forever. Alan Turing…
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 distinct intuitionistic logic, Gödel-Dummett logic incorporates a principle of maximal elements. This allows it to articulate specific intermediate truth…
Gödel numbering assigns unique natural numbers to symbols, formulas, and proofs in formal systems. This allows mathematical statements to be…
A frame in modal logic defines a set of possible worlds and the accessibility relation between them. It serves as…
A formula is a true or false expression in a formal language. It uses variables and logical connectives to construct…
A formal system is a set of symbols and rules for manipulating them, used to derive statements or theorems in…