Paper Citation Record · LEDGER

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words

As of 8 August 2026, this Paper Citation Record lists 55 of 55 outbound references and 0 inbound Pith citation observations for arXiv:2607.28116.

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pith.paper-citation-record.v1
2607.28116 v1

Coverage vector

measured 55 of 55 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-07-31T17:24:55.392185Z

measured 55 of 55 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Reference resolution

55 of 55 outbound references displayed

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Outbound references

Observation 3675a2f8-08b2-46ca-8bac-df8ec0a0a0cf · outbound

This paper cites Carlson-Simpson’s lemma and applications in reverse mathematics.Ann.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Carlson-Simpson’s lemma and applications in reverse mathematics.Ann

Reference 1

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Observation 42eadb65-3ae8-4b20-a938-16f898597247 · outbound

This paper cites Milliken's tree theorem and its applications: a computability-theoretic perspective.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Milliken's tree theorem and its applications: a computability-theoretic perspective

Reference 2

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Observation d0a181ec-d0d1-49f6-8fb7-c928841c004b · outbound

This paper cites Baumgartner.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Baumgartner

Reference 3

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Observation 47894858-0938-412b-a0fb-c0684ff3f1e2 · outbound

This paper cites Blass, Jeffry L.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Blass, Jeffry L

Reference 4

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Observation f3c726be-e8e2-4025-bf16-afe9da6d0ab3 · outbound

This paper cites The reverse mathe- matics of Carlson’s theorem for located words.J.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words The reverse mathe- matics of Carlson’s theorem for located words.J

Reference 5

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Observation ee6f381e-d102-4fa5-b116-bdbafe47e78b · outbound

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$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Unresolved cited work

Reference 6

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Observation b45e7127-c9c9-41a6-bc8a-ba758809e3e6 · outbound

This paper cites Carlson and Stephen G.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Carlson and Stephen G

Reference 7

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Observation 69dc1367-5fc9-4f2e-97e4-04e85febd55d · outbound

This paper cites The henson graphs: colorings and codings, 2026.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words The henson graphs: colorings and codings, 2026

Reference 8

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Observation 313327ca-5125-46dd-9691-6df526ac6b70 · outbound

This paper cites The finite big ram- sey degrees of henson graphs are provable in ACA 0, 2026.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words The finite big ram- sey degrees of henson graphs are provable in ACA 0, 2026

Reference 9

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Observation 0a715034-670c-44fd-8ab9-6660559d3140 · outbound

This paper cites an unresolved cited work.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Unresolved cited work

Reference 10

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Observation a438d05a-3100-4c67-9921-a3d360434b8e · outbound

This paper cites The Strength of Ramsey’s Theorem For Pairs over trees: IV.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words The Strength of Ramsey’s Theorem For Pairs over trees: IV

Reference 13

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Observation 2c78b8bd-cd71-4733-96db-c3fb3f1b7426 · outbound

This paper cites Conservation strength of the infinite pigeonhole principle for trees.Israel Journal of Mathematics, pages 1–24, 2023.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Conservation strength of the infinite pigeonhole principle for trees.Israel Journal of Mathematics, pages 1–24, 2023

Reference 14

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Observation cebaca49-a7c7-43e4-8b36-35ced7389dff · outbound

This paper cites Hirst, and Timothy H.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Hirst, and Timothy H

Reference 15

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Observation 35af8788-3859-474e-99f9-4c0e1b81ac15 · outbound

This paper cites Groszek, and Joseph R.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Groszek, and Joseph R

Reference 16

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Observation 2959c4d4-29e2-4020-bcab-5ba2b5ed180f · outbound

This paper cites ProQuest LLC, Ann Arbor, MI, 1980.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words ProQuest LLC, Ann Arbor, MI, 1980

Reference 17

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Observation bf3a109c-0300-476b-93c4-27c88bdb42ba · outbound

This paper cites The Ramsey theory of the universal homogeneous triangle-free graph.Journal of Mathematical Logic, 20(2):2050012, 75,.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words The Ramsey theory of the universal homogeneous triangle-free graph.Journal of Mathematical Logic, 20(2):2050012, 75,

Reference 18

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Observation 9ddaecbd-3ae1-4365-a969-e4a9068ef631 · outbound

This paper cites American Mathematical Society, Providence, RI, 2016.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words American Mathematical Society, Providence, RI, 2016

Reference 19

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Observation f5955bae-ae81-46e6-a051-14be703711c8 · outbound

This paper cites A den- sity version of the Carlson-Simpson theorem.J.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words A den- sity version of the Carlson-Simpson theorem.J

Reference 20

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Observation 32ccd23c-fa86-4e99-8a67-1d0179f874c9 · outbound

This paper cites Ef- fectiveness for the dual ramsey theorem.Notre Dame Journal of Formal Logic, 62(3):455–490, 2021.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Ef- fectiveness for the dual ramsey theorem.Notre Dame Journal of Formal Logic, 62(3):455–490, 2021

Reference 21

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Observation 57566261-06bf-46f8-a91a-5515d7deb69a · outbound

This paper cites Dzhafarov and Carl Mummert.Reverse mathematics—problems, reductions, and proofs.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Dzhafarov and Carl Mummert.Reverse mathematics—problems, reductions, and proofs

Reference 22

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Observation 8651fd98-f8be-48ac-96f6-c2e67d00e1b2 · outbound

This paper cites Dzhafarov and Ludovic Patey.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Dzhafarov and Ludovic Patey

Reference 23

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Observation af748cce-8f33-49e4-8318-4372a434229f · outbound

This paper cites Erd˝ os and G.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Erd˝ os and G

Reference 24

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Observation 27e97c6c-d3cd-400b-899a-c33fe786cb69 · outbound

This paper cites Personal communication to L.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Personal communication to L

Reference 25

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Observation d1267bb6-d3a8-46c7-be76-46e495d48be4 · outbound

This paper cites Graham, Bruce L.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Graham, Bruce L

Reference 26

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Observation 7362fb72-2e7d-4580-8903-0532853dd7b2 · outbound

This paper cites Perspectives in Mathematical Logic.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Perspectives in Mathematical Logic

Reference 27

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Observation 6e14c0ae-4442-4195-8dda-87eedd077b62 · outbound

This paper cites Finite sums from sequences within cells of a partition ofN.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Finite sums from sequences within cells of a partition ofN

Reference 28

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Observation ad69a168-2c18-4678-b1b7-cc428def2327 · outbound

This paper cites De Gruyter textbook.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words De Gruyter textbook

Reference 29

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Observation e8b3c0b6-6f59-4b56-9138-cc00fd9be627 · outbound

This paper cites ProQuest LLC, Ann Arbor, MI, 1987.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words ProQuest LLC, Ann Arbor, MI, 1987

Reference 30

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Observation 551581da-6879-40b9-a25b-cc265148e63f · outbound

This paper cites $\Pi^0_4$ conservation of the Ordered Variable Word theorem.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words $\Pi^0_4$ conservation of the Ordered Variable Word theorem

Reference 31

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Observation db697c6b-ad71-4b5c-9cb1-4e849385523e · outbound

This paper cites Largeness notions and polytime translation for@Σ 0 3-consequences ofRT 2 2, 2026.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Largeness notions and polytime translation for@Σ 0 3-consequences ofRT 2 2, 2026

Reference 32

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Observation 439920f2-22a0-42b4-b329-ad9e1b0a6236 · outbound

This paper cites Big Ramsey degrees using parameter spaces.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Big Ramsey degrees using parameter spaces

Reference 33

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Observation aeaf8237-7a38-443e-87e1-03465bbac541 · outbound

This paper cites The Clarendon Press, Oxford University Press, New York, 1991.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words The Clarendon Press, Oxford University Press, New York, 1991

Reference 34

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Observation 5f532184-52e3-412f-97c9-26d976183c74 · outbound

This paper cites Rapidly growing Ramsey functions.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Rapidly growing Ramsey functions

Reference 35

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Observation 14bcb76e-302c-45ea-8f12-6dcfeaae57ba · outbound

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$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Unresolved cited work

Reference 36

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Observation 64a750b1-edd5-46ae-861b-5b2d499c268a · outbound

This paper cites Ramsey’s theorem for pairs, collection, and proof size.Journal of Mathe- matical Logic, page 2350007, 2023.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Ramsey’s theorem for pairs, collection, and proof size.Journal of Mathe- matical Logic, page 2350007, 2023

Reference 37

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Observation 7e5f7714-7aae-4e16-8e5f-12916de37a19 · outbound

This paper cites Some upper bounds on ordinal-valued Ramsey numbers for colourings of pairs.Selecta Math.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Some upper bounds on ordinal-valued Ramsey numbers for colourings of pairs.Selecta Math

Reference 38

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Observation 3cf242cf-edd8-4221-bdd0-59d988a19559 · outbound

This paper cites Π 0 4 con- servation of Ramsey’s theorem for pairs.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Π 0 4 con- servation of Ramsey’s theorem for pairs

Reference 39

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Observation a0a1a91e-f8e6-4725-9f43-9aca4e0d16d2 · outbound

This paper cites Corrigendum to: Π 0 4 conservation of Ramsey’s theorem for pairs.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Corrigendum to: Π 0 4 conservation of Ramsey’s theorem for pairs

Reference 40

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Observation fa7f86d3-6252-4544-92fc-e68e47d2cf0b · outbound

This paper cites Π0 4 conser- vation of ramsey’s theorem for pairs.Journal of the London Mathematical Society, 113(1):e70419, 2026.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Π0 4 conser- vation of ramsey’s theorem for pairs.Journal of the London Mathematical Society, 113(1):e70419, 2026

Reference 41

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Observation 97e6d72a-23a0-4c4d-922a-dea2e7cdf1a3 · outbound

This paper cites A computable analysis of vari- able words theorems.Proc.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words A computable analysis of vari- able words theorems.Proc

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Observation 5a1f337f-85b2-4624-8271-09ba5e11c34e · outbound

This paper cites The reverse mathematics of the ordered variable word theorem.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words The reverse mathematics of the ordered variable word theorem

Reference 43

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Observation 66a9349a-775b-4b2b-8d26-d2a6184d5e3c · outbound

This paper cites Miller and Reed Solomon.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Miller and Reed Solomon

Reference 44

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Observation 79c51635-306d-4f6e-839a-2670bba2f8c8 · outbound

This paper cites Milliken.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Milliken

Reference 45

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Observation 9f3b5388-ce8a-498d-b8e6-16875417b1cf · outbound

This paper cites The strength of the tree theorem for pairs in reverse math- ematics.J.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words The strength of the tree theorem for pairs in reverse math- ematics.J

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Observation d3732f38-eb9c-4c1a-83db-051fa4b6148e · outbound

This paper cites The proof-theoretic strength of Ram- sey’s theorem for pairs and two colors.Adv.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words The proof-theoretic strength of Ram- sey’s theorem for pairs and two colors.Adv

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Observation 8988817a-a7f1-4a89-9aa2-bc8e6660cbe6 · outbound

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$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Unresolved cited work

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Observation 8c4dd2d2-c07c-42cb-aeac-b195fa3aa9cf · outbound

This paper cites Algebras of sets binumerable in complete extensions of arith- metic.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Algebras of sets binumerable in complete extensions of arith- metic

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Observation 03427da6-17a3-48dd-825a-85c88916a772 · outbound

This paper cites Primitive recursive bounds for van der Waerden numbers.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Primitive recursive bounds for van der Waerden numbers

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Observation c67ccfcf-c539-4f07-899f-3cb7e7f14858 · outbound

This paper cites Simpson.Subsystems of second order arithmetic.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Simpson.Subsystems of second order arithmetic

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Observation 94d70965-ecae-4b91-87e9-12f84e1096fa · outbound

This paper cites Princeton University Press, Princeton, NJ, 2010.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Princeton University Press, Princeton, NJ, 2010

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Observation d1cb07c8-bcbd-44a5-af9b-e3f6f10cbfbe · outbound

This paper cites Hindman’s theorem: an ultrafilter argument in second order arithmetic.J.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Hindman’s theorem: an ultrafilter argument in second order arithmetic.J

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Observation 2a411170-e723-4b96-85be-62b2e7812d61 · outbound

This paper cites A simple proof and some difficult examples for Hindman’s theorem.Notre Dame J.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words A simple proof and some difficult examples for Hindman’s theorem.Notre Dame J

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Observation afa29bd2-813b-494d-98e6-de6e91f6370f · outbound

This paper cites Erd˝ os-moser andIΣ 2.Israel J.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Erd˝ os-moser andIΣ 2.Israel J

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Observation 0ef976c3-193c-4f93-9e5b-f868c474aeb4 · outbound

This paper cites The Strength of Ramsey's Theorem For Pairs over trees: I. Weak K\"onig's Lemma.

$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words The Strength of Ramsey's Theorem For Pairs over trees: I. Weak K\"onig's Lemma

Reference 2019

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Observation 2dd0cdfd-945a-4501-b65f-36e2c91d1acf · outbound

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$\Pi^0_4$ conservation of a Carlson-Simpson lemma for 1-variable words Unresolved cited work

Reference 2020

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