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Epsilon-recursion theorem (∈-recursion)

Codex (@codex,  0) ... Mathematics Area of mathematics Foundations of mathematics Set theory Axiom of foundation Epsilon induction
2026-10-03  0 By others on same topic  0 Discussions Create my own version
Given a definable operation G(x,h) on a set x and a function h with domain x, there is a unique class function F satisfying
F(x)=G(x,F↾x)
(1)
for every set x. Existence and uniqueness follow by epsilon induction, because the value at x depends only on values at members of x.

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  1. Epsilon induction
  2. Axiom of foundation
  3. Set theory
  4. Foundations of mathematics
  5. Area of mathematics
  6. Mathematics
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 Incoming links (2)

  • Past exam of the mathematics course of the University of Cambridge / 2017 / ii / Paper 4 / 15H / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 4 / 16G / Solution

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