Pith Number

pith:RJZIRKNU

pith:2026:RJZIRKNU7I6A2PVDPWWUGQDRPM

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Model-theoretic Tameness in finite extensions of groups

Saharon Shelah, Yatir Halevi

There exists an ω-stable group whose finite-index extensions and subgroups interpret any countable first-order structure.

arxiv:2605.14390 v1 · 2026-05-14 · math.LO · math.GR

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\usepackage{pith}
\pithnumber{RJZIRKNU7I6A2PVDPWWUGQDRPM}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

there exists an ω-stable group G such that any given countable first-order structure in a finite language is interpretable both in some finite-index extension of G and in some finite-index subgroup of G.

C2weakest assumption

The existence of a specific ω-stable group G whose finite-index extensions and subgroups allow interpretation of arbitrary countable structures, which depends on the details of the construction provided in the paper.

C3one line summary

There exists an ω-stable group G such that every countable structure in a finite language is interpretable in some finite-index extension and some finite-index subgroup of G.

References

19 extracted · 19 resolved · 0 Pith anchors

[1] John T. Baldwin. Some notes on stable groups. In The model theory of groups ( N otre D ame, IN , 1985--1987) , volume 11 of Notre Dame Math. Lectures , pages 100--116. Univ. Notre Dame Press, Notre Da 1985

[2] A. Baudisch. Subgroups of semifree groups. Acta Math. Acad. Sci. Hungar. , 38(1-4):19--28, 1981 1981

[3] I. M. Chiswell. Ordering graph products of groups. Internat. J. Algebra Comput. , 22(4):1250037, 14, 2012 2012

[4] First-order aspects of artin groups 2025

[5] Ordered groups and topology , volume 176 of Graduate Studies in Mathematics 2016

Receipt and verification

First computed	2026-05-17T23:39:07.624386Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8a7288a9b4fa3c0d3ea37dad4340717b1954ecc79f2e4f2527e3833be0e92444

Aliases

arxiv: 2605.14390 · arxiv_version: 2605.14390v1 · doi: 10.48550/arxiv.2605.14390 · pith_short_12: RJZIRKNU7I6A · pith_short_16: RJZIRKNU7I6A2PVD · pith_short_8: RJZIRKNU

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/RJZIRKNU7I6A2PVDPWWUGQDRPM \
  | 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: 8a7288a9b4fa3c0d3ea37dad4340717b1954ecc79f2e4f2527e3833be0e92444

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a70c698b6e1c98c347d9e5541cd0e30f1b2100f48a9e9f6bf743742b5e5eb45d",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2026-05-14T05:12:44Z",
    "title_canon_sha256": "07cb5164488e7e4b8771266fe1c152905901be1d73fc7fbfa7d8c899137993b1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14390",
    "kind": "arxiv",
    "version": 1
  }
}