{
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  "body": "\n## Problem\n\nIs there a [[computably enumerable set|TN9G24VABN]] $A \\subseteq \\N$ that is not computable and is not [[Turing equivalent|PA4PYQ1PZ0]] to the [[halting problem|Z7TN2B35B0]]?\nIn terms of [[Turing degrees|P5N2ND3VCG]]: is there a computably enumerable degree $\\mathbf{a}$ with $\\mathbf{0} \u003c \\mathbf{a} \u003c \\mathbf{0}'$?\n\n## Remarks\n\nEvery computably enumerable set $A$ satisfies $A \\le_T \\emptyset'$, so the question asks whether the c.e. degrees contain anything besides $\\mathbf{0}$ and $\\mathbf{0}'$.\nEmil Post posed the question in 1944.\nThe answer is yes.\nFriedberg and Muchnik answered it independently, in 1957 and 1956, by constructing two c.e. sets that are not Turing reducible to each other; see the [[Friedberg–Muchnik theorem|RA358M9QCN]].\nTheir method of construction is the [[priority method|3BZFSC5QZ2]].\nPost's own attempt was to find a structural property of c.e. sets, such as being simple, that forces the degree to lie strictly between $\\mathbf{0}$ and $\\mathbf{0}'$.\n\n## Explanations\n\n### L1 human\n\nAmong the sets that a computer can list, the easiest are the ones it can also decide, and the hardest is the set of halting programs.\nPost asked whether anything lies in between.\nIt took more than ten years and a new technique to show that the answer is yes.\n",
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      "first_stated": "1944",
      "posed_by": "Emil Post"
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      "03D25",
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    "name": "Post's problem",
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    "tag": "1RVF7DWG8C",
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      "P5N2ND3VCG"
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  "link": "https://math2.tamnd.com/node/1RVF7DWG8C/",
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  "msc": [
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  "name": "Post's problem",
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  "source": "https://github.com/tamnd/math2/blob/main/nodes/1RV/1RVF7DWG8C.md",
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