Lawvere's fixed-point theorem

In mathematics, Lawvere's fixed-point theorem is an important result in category theory.[1] It is a broad abstract generalization of many diagonal arguments in mathematics and logic, such as Cantor's diagonal argument, Russell's paradox, Gödel's first incompleteness theorem and Turing's solution to the Entscheidungsproblem.[2]

It was first proven by William Lawvere in 1969.[3][4]

  1. ^ Soto-Andrade, Jorge; J. Varela, Francisco (1984). "Self-Reference and Fixed Points: A Discussion and an Extension of Lawvere's Theorem". Acta Applicandae Mathematicae. 2. doi:10.1007/BF01405490.
  2. ^ Yanofsky, Noson (September 2003). "A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points". The Bulletin of Symbolic Logic. 9 (3): 362–386. arXiv:math/0305282. doi:10.2178/bsl/1058448677.
  3. ^ Lawvere, Francis William (1969). "Diagonal arguments and Cartesian closed categories". Category Theory, Homology Theory and their Applications II (Lecture Notes in Mathematics, vol 92). Berlin: Springer.
  4. ^ Lawvere, William (2006). "Diagonal arguments and cartesian closed categories with author commentary". Reprints in Theory and Applications of Categories (15): 1–13.