{
  "aliases": [
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  "body": "\n## Summary\n\nIn set theory and logic, **Buchholz's ID hierarchy** is a hierarchy of subsystems of [[first-order arithmetic|0QFT7Z76N5]]. The systems/theories $\\mathsf{ID}_\\nu$ are referred to as \"the formal theories of *ν*-times iterated inductive definitions\". ID\u003csub\u003e*ν*\u003c/sub\u003e extends [[PA|0QFT7Z76N5]] by *ν* iterated least fixed points of monotone operators.\n",
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      {
        "what": "edge defines in",
        "note": "at least one definition",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
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        "what": "edge not_instance_of in",
        "note": "at least one non-example",
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        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
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