Pith Number

pith:4C7B65PR

pith:2026:4C7B65PRVHIQIVBKXYH2UH2QUU

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On the Intermediate Models of Strongly Compact Prikry Forcing

Ben-Zion Weltsch, Sebastiano Thei, Tom Benhamou

A simple combinatorial property characterizes all projections of the strongly compact Prikry forcing using κ-complete fine measures.

arxiv:2605.09161 v2 · 2026-05-09 · math.LO

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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

We exhibit a simple combinatorial property which, for a given supercompact cardinal κ, characterize the projections of all projections of the strongly compact Prikry forcing using κ-complete fine measures.

C2weakest assumption

The existence of a κ-complete fine measure U on P_κ(λ) (or the assumption that κ is 2^λ-strongly compact) together with the standard properties of Prikry forcing conditions.

C3one line summary

The authors characterize projections of strongly compact Prikry forcing using κ-complete fine measures, generalize prior results on κ-distributive forcings, and give Rudin-Keisler-style criteria for projections.

Receipt and verification

First computed	2026-06-04T01:09:50.668211Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0be1f75f1a9d104542abe0faa1f50a517cc9979ce2f04a0c6d7c914af749134

Aliases

arxiv: 2605.09161 · arxiv_version: 2605.09161v2 · doi: 10.48550/arxiv.2605.09161 · pith_short_12: 4C7B65PRVHIQ · pith_short_16: 4C7B65PRVHIQIVBK · pith_short_8: 4C7B65PR

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/4C7B65PRVHIQIVBKXYH2UH2QUU \
  | 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: e0be1f75f1a9d104542abe0faa1f50a517cc9979ce2f04a0c6d7c914af749134

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fc25ccd4548ccd0bdca4d802461aa3f651221d1998e3dbb39f7952a4319dd029",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2026-05-09T20:47:44Z",
    "title_canon_sha256": "5608e4404324e6a9b00d62886a2555195bea0970879977bbd9cea8e5b8ec31d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.09161",
    "kind": "arxiv",
    "version": 2
  }
}