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Edgepedia / Physical world and mathematics / Mathematics and statistics / Logic and discrete mathematics / Formal logic and foundations / Computability theory

Recursion theorem and self-reference

2 articles

GeneralSep 17, 2026

Kleene's recursion theorem

Kleene's recursion theorem, also called the fixed point theorem, is a result in computability theory published by Stephen Kleene in 1938, implying self-reproducing programs called quines.

GeneralOct 15, 2026

Recursion theorem fixed point

In computability theory, a recursion theorem fixed point is a program index n with the same partial function as its transform, φn = φf(n), guaranteed by Kleene's second recursion theorem.

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