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Fixed-Point Theorems in Analysis, Logic, and Computer Science
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A brief survey of some fixed-point theorems in mathematics, including:
- Banach's fixed-point theorem (the contraction mapping theorem)
- Gödel / Carnap's fixed-point lemma (the diagonal lemma), with an application to Gödel's first incompleteness theorem for Peano arithmetic
- Fixed-point combinators of Curry (Y combinator) and Turing (Theta combinator) in the lambda calculus
- Banach's fixed-point theorem (the contraction mapping theorem)
- Gödel / Carnap's fixed-point lemma (the diagonal lemma), with an application to Gödel's first incompleteness theorem for Peano arithmetic
- Fixed-point combinators of Curry (Y combinator) and Turing (Theta combinator) in the lambda calculus
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