Pith Number

pith:UU4NYTSY

pith:2026:UU4NYTSYFOTQ2UCEVEN7GM5VY5

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O-minimal open core is not an elementary property

Alexi Block Gorman, Esther Elbaz Saban

Having an o-minimal open core is not an elementary property.

arxiv:2605.13683 v1 · 2026-05-13 · math.LO

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\pithnumber{UU4NYTSYFOTQ2UCEVEN7GM5VY5}

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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

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Claims

C1strongest claim

we prove that having an o-minimal open core is not an elementary property. In particular, we construct an expansion of the structure (Q,<) that has an o-minimal open core, but some of its elementary superstructures do not.

C2weakest assumption

That the specific expansion of (Q,<) can be chosen so its open core is o-minimal while some elementary extension has a non-o-minimal open core; this relies on the construction preserving the necessary first-order properties.

C3one line summary

O-minimality of the open core is not an elementary property, shown via a counterexample expansion of (Q, <) whose elementary superstructures can lack the property.

References

9 extracted · 9 resolved · 0 Pith anchors

[1] Alexi Block Gorman, Philipp Hieronymi, and Elliot Kaplan, Pairs of Theories Satisfying a Mordell-Lang Condition. Fund. Math., (2) 251:131-160, (2020) 2020

[2] Gareth Boxall and Philipp Hieronymi, Expansions which introduce no new open sets.J. Symb. Log., 77(1):111-121, (2012) 2012

[3] Alfred Dolich, Chris Miller, and Charles Steinhorn, Structures having o-minimal open core.Trans. Am. Math. Soc., 362(3):1371–1411, (2010) 2010

[4] Alfred Dolich, Chris Miller, and Charles Steinhorn, Expansions of o-minimal structures by dense independent sets.Ann. Pure Appl. Logic, 167(8):684–706, (2016) 2016

[5] Philipp Hieronymi, Travis Nell, and Erik Walsberg, Wild theories with o-minimal open core.Ann. Pure Appl. Logic, (2) 169:146–163, (2018) 2018

Receipt and verification

First computed	2026-05-18T02:44:17.016208Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a538dc4e582ba70d5044a91bf333b5c746e10b927de7a7d465cba5f412da95fa

Aliases

arxiv: 2605.13683 · arxiv_version: 2605.13683v1 · doi: 10.48550/arxiv.2605.13683 · pith_short_12: UU4NYTSYFOTQ · pith_short_16: UU4NYTSYFOTQ2UCE · pith_short_8: UU4NYTSY

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/UU4NYTSYFOTQ2UCEVEN7GM5VY5 \
  | 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: a538dc4e582ba70d5044a91bf333b5c746e10b927de7a7d465cba5f412da95fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "89bef574563cf71890aabfd3b0e6036370373b054079d2fbfa8550167bdb614b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2026-05-13T15:40:59Z",
    "title_canon_sha256": "2083b3332ed3074063e6d5a12257c76f8cdac59602e3921f4fdeb7f683b1e3d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13683",
    "kind": "arxiv",
    "version": 1
  }
}