Pith Number

pith:F7WHYRHY

pith:2025:F7WHYRHYBPG46BWHDPRUEE5GVV

not attested not anchored not stored refs resolved

On the isomorphism problem for ultraproducts of $\mathrm{C}^*$-algebras in continuous model theory

Akihiko Arai

Assuming the negation of the continuum hypothesis, there exist elementarily equivalent C*-algebras of density at most c whose ultrapowers are never isomorphic.

arxiv:2511.15867 v3 · 2025-11-19 · math.OA · math.LO

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4 Citations open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

assuming the negation of the continuum hypothesis, there exist two elementarily equivalent infinite-dimensional unital C*-algebras A and B, whose density characters are at most c, such that for all non-principal ultrafilters U, V on ω, the ultrapowers A^U and B^V are not isomorphic.

C2weakest assumption

The existence of two elementarily equivalent C*-algebras A and B (with the stated size bound) whose ultrapowers remain non-isomorphic for every choice of non-principal ultrafilters, which the abstract presents as following from the negation of CH but whose concrete construction is not visible in the abstract.

C3one line summary

Assuming the negation of the continuum hypothesis, there exist elementarily equivalent C*-algebras A and B such that A^U and B^V are non-isomorphic for every pair of non-principal ultrafilters U and V on omega.

References

32 extracted · 32 resolved · 0 Pith anchors

[1] Ward Henson, and Alexander Usvyatsov 2008

[2] Theory ofC ∗-algebras and von Neumann alge- bras, volume 122 ofEncyclopaedia of Mathematical Sciences

[3] Operator Algebras and Non-commutative Geometry, III

[4] C. C. Chang and H. Jerome Keisler.Model theory, volume 73 ofStudies in Logic and the Foundations of Mathematics. North-Holland Publishing Co., Amsterdam, third edition, 1990 1990

[5] Jerome Keisler.Continuous model theory, volume 58 of Annals of Mathematics Studies 1966

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:32.406856Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2fec7c44f80bcdcf06c71be34213a6ad618850f457a0fa00dfe1538c4a7ae082

Aliases

arxiv: 2511.15867 · arxiv_version: 2511.15867v3 · doi: 10.48550/arxiv.2511.15867 · pith_short_12: F7WHYRHYBPG4 · pith_short_16: F7WHYRHYBPG46BWH · pith_short_8: F7WHYRHY

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/F7WHYRHYBPG46BWHDPRUEE5GVV \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 2fec7c44f80bcdcf06c71be34213a6ad618850f457a0fa00dfe1538c4a7ae082

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e706e9c6915fd0d02016f497bbc5ee42741bdbf23fbd60452e517cb67fac5eb5",
    "cross_cats_sorted": [
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2025-11-19T20:44:46Z",
    "title_canon_sha256": "97049198060f056d24206fda8650e069929c54ec44463f8b35dd16d4e62b5353"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2511.15867",
    "kind": "arxiv",
    "version": 3
  }
}