{
  "aliases": null,
  "backlinks": [
    {
      "field": "uses",
      "target": "1513J40TKA"
    },
    {
      "field": "defines",
      "target": "HJBYFPJEQ1"
    },
    {
      "field": "instance_of",
      "target": "RMXR0FEF54"
    }
  ],
  "body": "\n## Summary\n\nA Fraïssé limit of a class of finitely generated structures is a countable structure that is as symmetric as possible.\nIts finitely generated substructures are exactly the members of the class, up to isomorphism.\nHere \"as symmetric as possible\" means ultrahomogeneous: every isomorphism between finitely generated substructures extends to an automorphism.\nFraïssé's theorem gives existence and uniqueness up to isomorphism under four conditions.\nThe class must have the hereditary, joint embedding and [[amalgamation|XSCSX39GEZ]] properties, and only countably many isomorphism types.\nThe rational numbers with their order and the [[Rado graph|RMXR0FEF54]] are the standard examples.\n\n## Explanations\n\n### L1 human\n\nStart with a collection of small pieces, such as all finite linear orders or all finite graphs.\nThe Fraïssé limit is one countable object into which every piece fits, and in which any two copies of the same piece look alike from the outside.\nFor finite linear orders the limit is $(\\Q, \u003c)$.\nEvery finite order sits inside $\\Q$, and any order-preserving map between two finite subsets of $\\Q$ extends to an order-preserving bijection of all of $\\Q$.\n",
  "commit": "547b6eddb8f2feb8d579f2d633d22a27b7e132fc",
  "front": {
    "kind": "concept",
    "msc": [
      "03C15",
      "03C52"
    ],
    "name": "Fraïssé limit",
    "same_as": {
      "wikidata": "Q85850626",
      "wikipedia": "Fraïssé limit"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Fraïssé_limit"
      }
    ],
    "tag": "HJVRBDQSGG"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/HJVRBDQSGG/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/HJVRBDQSGG.md",
  "msc": [
    "03C15",
    "03C52"
  ],
  "name": "Fraïssé limit",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/HJV/HJVRBDQSGG.md",
  "status": null,
  "tag": "HJVRBDQSGG",
  "uri": "m2://HJVRBDQSGG",
  "url": "https://math2.tamnd.com/wiki/fraisse-limit/",
  "writing": {
    "tag": "HJVRBDQSGG",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}