{
  "id": "1109.2246",
  "version": "v2",
  "published": "2011-09-10T18:18:35.000Z",
  "updated": "2011-10-11T14:26:20.000Z",
  "title": "Pseudofinite and pseudocompact metric structures",
  "authors": [
    "Isaac Goldbring",
    "Vinicius Cifu Lopes"
  ],
  "comment": "Second version. Some typos fixed. Easier proofs in Section 5",
  "categories": [
    "math.LO"
  ],
  "abstract": "We initiate the study of pseudofiniteness in continuous logic. We introduce a related concept, namely that of pseudocompactness, and investigate the relationship between the two concepts. We establish some basic properties of pseudofiniteness and pseudocompactness and provide many examples. We also investigate the injective-surjective phenomenon for definable endofunctions in pseudofinite structures.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-10-11T14:26:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "pseudocompact metric structures",
      "basic properties",
      "pseudocompactness",
      "pseudofiniteness",
      "pseudofinite structures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.2246G"
    }
  }
}