A formal logic and mathematics proof technique. It verifies properties for basic formulas and ensures they are maintained through operations…
The property of a logical or mathematical system where not all true statements can be proven within the system's own…
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 self-referential sentence in formal systems, a Gödel sentence demonstrates incompleteness theorems by asserting its own unprovability within that system.…
Gödel numbering assigns unique natural numbers to symbols, formulas, and proofs in formal systems. This allows mathematical statements to be…
Finite character describes systems where all essential properties can be understood by analyzing a limited, finite portion. This concept is…
A finitary formal system uses only finite operations, proofs, and expressions. It relies on objects constructible in a finite number…
Finitary arithmetic is a mathematical approach that emphasizes constructive methods, avoiding infinite concepts. It focuses on operations and proofs that…