{
  "annotation_id": "353dd051-4204-49cc-b94b-e0afa0e33bfc",
  "date_created": "2026-02-17T05:53:08.574000Z",
  "date_modified": "2026-02-17T05:53:08.574000Z",
  "file_hash": "4e7a4054c7bb90ae0bcb8a69ef8bbfd99617711b7aca977aa0a62a57bf792974",
  "private": false,
  "record": {
    "abstract": "We introduce pseudofinite W*-probability spaces. These are W*-probability spaces that are elementarily equivalent to Ocneanu ultraproducts of finite-dimensional von Neumann algebras equipped with arbitrary faithful normal states. We are particularly interested in the case where these finite-dimensional von Neumann algebras are full matrix algebras: the pseudofinite factors. We show that these are indeed factors. We see as a consequence that pseudofinite factors are never of type $\\mathrm{III}_0$. Mimicking the construction of the Powers factors, we give explicit families of examples of matrix algebra ultraproducts that are $\\mathrm{III}_\\lambda$ factors for $\\lambda \\in (0,1]$. We show that these examples share their universal theories with the corresponding Powers factor and thus have uncomputable universal theories. Finally, we show that pseudofinite factors are full. This generalizes a theorem of Farah-Hart-Sherman which shows that pseudofinite tracial factors do not have property $\\Gamma$. It has the consequence that hyperfinite factors of type $\\mathrm{III}$ (the Powers factors) are never pseudofinite. Our proofs combine operator algebraic insights with routine continuous logic syntactic arguments: using \\L os\u0027 theorem to prove that certain sentences which are true for all matrix algebras are inherited by their ultraproducts.",
    "arxiv_id": "2601.06455",
    "authors": [
      "Jananan Arulseelan"
    ],
    "categories": [
      "math.OA",
      "math.LO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "A Note on Pseudofinite W*-Probability Spaces",
    "url": "https://arxiv.org/abs/2601.06455",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "aa1bee15-7163-4cce-9ed9-bb1d5550a59d",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}