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Paper Citation Record · LEDGER

Some applications of the real strict order property hierarchy

As of 19 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 1 inbound Pith citation observation for arXiv:2606.28740.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2606.28740 v2

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-12T11:20:25.093177Z

measured 37 of 37 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-14T14:42:44.054549Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-08-14T14:42:44.118563Z

Reference resolution

36 of 36 outbound references displayed

  • verified exact0
  • verified fuzzy0
  • unresolved36
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 6218c1c3-4d2f-4915-bf44-bf8c0d5b4443 · outbound

This paper cites Preservation ofNATP.Journal of Mathematical Logic, 25(01):2450012, 2025.

Some applications of the real strict order property hierarchy Preservation ofNATP.Journal of Mathematical Logic, 25(01):2450012, 2025

Reference 1

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source=pdf_text observed=2026-07-12T11:20:25.093177Z digest=sha256:be5fe3c56d98bfbe4178f9468eee2b83fec4c1ab2cc8f706deb9f2b3a8b5cbbb

Observation 01bc0d0d-88e1-430a-bab6-1baac26f5135 · outbound

This paper cites A Walk on the Wild Side: Notions of maximality in first-order theories.

Some applications of the real strict order property hierarchy A Walk on the Wild Side: Notions of maximality in first-order theories

Reference 2

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source=pdf_text observed=2026-07-12T11:20:25.093177Z digest=sha256:24e2e4cdabb919bb636b2e21d6eccc1bb5e67e2d5f1a10204b2654434210e71f

Observation a10873bf-1a20-4d5c-9afd-c3c3555e6a59 · outbound

This paper cites Taking model-complete cores, Preprint.

Some applications of the real strict order property hierarchy Taking model-complete cores, Preprint

Reference 3

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Observation bab69f4a-62f4-4ca3-885f-1f05a6ec7d96 · outbound

This paper cites More on tree properties.Fundamenta Mathematicae, 2019.

Some applications of the real strict order property hierarchy More on tree properties.Fundamenta Mathematicae, 2019

Reference 4

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Observation bfafa542-d30b-47cd-984f-a6ebafeb010f · outbound

This paper cites an unresolved cited work.

Some applications of the real strict order property hierarchy Unresolved cited work

Reference 5

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Observation c7abdcd1-8a30-4b34-be74-05769f655388 · outbound

This paper cites Universal graphs with forbidden subgraphs and algebraic closure.Advances in Applied Mathematics, 22(4):454–491, 1999.

Some applications of the real strict order property hierarchy Universal graphs with forbidden subgraphs and algebraic closure.Advances in Applied Mathematics, 22(4):454–491, 1999

Reference 6

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Observation c33451fc-f30a-4748-ab96-2e4fde6bb636 · outbound

This paper cites Theories without the tree property of the second kind.Ann.

Some applications of the real strict order property hierarchy Theories without the tree property of the second kind.Ann

Reference 7

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Observation bc01db1c-fb0d-405f-a2c8-9843fc985be0 · outbound

This paper cites Forking and dividing inNTP 2 theories.The Journal of Symbolic Logic, 77(1):1–20, 2012.

Some applications of the real strict order property hierarchy Forking and dividing inNTP 2 theories.The Journal of Symbolic Logic, 77(1):1–20, 2012

Reference 8

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Observation 3b4957a3-bc71-46cf-ab24-5d9e8dc71beb · outbound

This paper cites On model-theoretic tree properties.Journal of Mathematical Logic, 16(2):1650009, 2016.

Some applications of the real strict order property hierarchy On model-theoretic tree properties.Journal of Mathematical Logic, 16(2):1650009, 2016

Reference 9

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Observation d9a27691-516a-4346-8393-d06f632df0f4 · outbound

This paper cites Independence in generic incidence structures.The Journal of Symbolic Logic, 84(2):750–780, 2019.

Some applications of the real strict order property hierarchy Independence in generic incidence structures.The Journal of Symbolic Logic, 84(2):750–780, 2019

Reference 10

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Observation 8c664706-14fd-4c3d-859f-0cdb3503625a · outbound

This paper cites On the notion of a patterning property in model theory.

Some applications of the real strict order property hierarchy On the notion of a patterning property in model theory

Reference 11

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Observation 698eb018-7830-497e-b3b5-66b9cc5ba7fe · outbound

This paper cites On◁ ∗-maximality.Annals of Pure and Applied Logic, 125(1-3):119–158, 2004.

Some applications of the real strict order property hierarchy On◁ ∗-maximality.Annals of Pure and Applied Logic, 125(1-3):119–158, 2004

Reference 12

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Observation 7990dbae-c5a3-4670-8d76-564eb6ff1552 · outbound

This paper cites an unresolved cited work.

Some applications of the real strict order property hierarchy Unresolved cited work

Reference 13

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Observation c76ef034-6289-42fb-8c54-46daffc11243 · outbound

This paper cites Hanson-SOP r,.

Some applications of the real strict order property hierarchy Hanson-SOP r,

Reference 14

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Observation bab7c838-beae-4c47-b7b3-9397521b3be6 · outbound

This paper cites On Kim-independence.Journal of the European Mathematical Society, 22, 02 2017.

Some applications of the real strict order property hierarchy On Kim-independence.Journal of the European Mathematical Society, 22, 02 2017

Reference 15

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Observation 0b08a77b-6643-47bc-9a01-302cc52dddd7 · outbound

This paper cites Transitivity of Kim-independence.Advances in Mathematics, 379:107573, 2021.

Some applications of the real strict order property hierarchy Transitivity of Kim-independence.Advances in Mathematics, 379:107573, 2021

Reference 16

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Observation e9df80a8-8d2a-443a-9b15-3365d6232cd8 · outbound

This paper cites Generic Stability Independence and Treeless theories.

Some applications of the real strict order property hierarchy Generic Stability Independence and Treeless theories

Reference 17

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Observation 6b10a9c7-2832-45e1-9d43-c7b94d27593e · outbound

This paper cites SomeNIP-like phenomena inNTP 2.arXiv: Logic, 2017.

Some applications of the real strict order property hierarchy SomeNIP-like phenomena inNTP 2.arXiv: Logic, 2017

Reference 18

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source=pdf_text observed=2026-07-12T11:20:25.093177Z digest=sha256:91e9e299a6ea4cfad5faae08e0eb5bd6cdf8c3d070738f93091b998204f86f75

Observation 16d31c9b-a624-4705-958b-476a198e85b3 · outbound

This paper cites Forking in Simple Unstable Theories.Journal of the London Mathematical Society, 57(2):257–267, 04 1998.

Some applications of the real strict order property hierarchy Forking in Simple Unstable Theories.Journal of the London Mathematical Society, 57(2):257–267, 04 1998

Reference 19

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Observation ce67b5a3-9ee9-48a4-b007-88d9ec0b7208 · outbound

This paper cites The structure and the number ofP7-free bipartite graphs.European Journal of Combinatorics, 65:143–153, 2017.

Some applications of the real strict order property hierarchy The structure and the number ofP7-free bipartite graphs.European Journal of Combinatorics, 65:143–153, 2017

Reference 20

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Observation 2e44b8f7-5b23-4802-896b-620552f22785 · outbound

This paper cites an unresolved cited work.

Some applications of the real strict order property hierarchy Unresolved cited work

Reference 21

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Observation 0beee0d7-73d2-4234-a22e-29a4a5bb0b0e · outbound

This paper cites Malliaris.

Some applications of the real strict order property hierarchy Malliaris

Reference 22

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source=pdf_text observed=2026-07-12T11:20:25.093177Z digest=sha256:55bd87a108f7bff09d8d7d6ac2d3dae2a9eea14d5f5e05938ed1495db4788eb8

Observation a2d8ad80-c1a1-4ad6-95b4-5a750ce29d72 · outbound

This paper cites Categoricity in power.Transactions of the American Mathematical Society, 114(2):514–538, 1965.

Some applications of the real strict order property hierarchy Categoricity in power.Transactions of the American Mathematical Society, 114(2):514–538, 1965

Reference 23

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Observation e4522737-e460-4092-b32a-c88b297aa1f6 · outbound

This paper cites Conant-independence and generalized free amalgamation.Journal of Mathematical Logic, 2024.

Some applications of the real strict order property hierarchy Conant-independence and generalized free amalgamation.Journal of Mathematical Logic, 2024

Reference 24

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Observation 716d07bf-ace4-40df-ba39-93769b04e098 · outbound

This paper cites On NSOP 2 theories.Journal of the European Mathematical Society, 27(11):3475–3544, 2025.

Some applications of the real strict order property hierarchy On NSOP 2 theories.Journal of the European Mathematical Society, 27(11):3475–3544, 2025

Reference 25

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Observation c9980b21-7756-4a6e-9db2-127d21f9a6bd · outbound

This paper cites Approximations of the strict order property, preprint.

Some applications of the real strict order property hierarchy Approximations of the strict order property, preprint

Reference 26

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Observation 60be3133-2a3d-43b9-a111-21350bfc9c4c · outbound

This paper cites Properties of independence in $\mathrm{NSOP}_3$ theories.

Some applications of the real strict order property hierarchy Properties of independence in $\mathrm{NSOP}_3$ theories

Reference 27

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Observation e039f448-88eb-4e95-b1b9-b14a1bfe4eb7 · outbound

This paper cites Saracino.

Some applications of the real strict order property hierarchy Saracino

Reference 28

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Observation a3c333f4-a942-40af-8e2f-813f87c10b0a · outbound

This paper cites Elsevier, 1990.

Some applications of the real strict order property hierarchy Elsevier, 1990

Reference 29

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Observation ba24476b-a113-40a6-9554-5fd12f41b2f9 · outbound

This paper cites The universality spectrum: Consistency for more classes in combinatorics, paul erd ¨os is eighty, vol.

Some applications of the real strict order property hierarchy The universality spectrum: Consistency for more classes in combinatorics, paul erd ¨os is eighty, vol

Reference 30

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source=pdf_text observed=2026-07-12T11:20:25.093177Z digest=sha256:cdeb8d1d0b98e350772cfc139dff3bf5d442282c54b42a25b92548da81829228

Observation 570bcb6d-9f0f-4026-9d19-55ea16532416 · outbound

This paper cites Toward classifying unstable theories.Annals of Pure and Applied Logic, 80(3):229–255, 1996.

Some applications of the real strict order property hierarchy Toward classifying unstable theories.Annals of Pure and Applied Logic, 80(3):229–255, 1996

Reference 31

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Observation e30960a5-844f-4478-8ebc-6fc37d28827c · outbound

This paper cites On what I do not understand (and have something to say), model theory.

Some applications of the real strict order property hierarchy On what I do not understand (and have something to say), model theory

Reference 32

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Observation e4cd43e3-574e-46a9-bc95-a0a78fb8b33e · outbound

This paper cites More onSOP 1 andSOP 2.Annals of Pure and Applied Logic, 155(1):16–31, 2008.

Some applications of the real strict order property hierarchy More onSOP 1 andSOP 2.Annals of Pure and Applied Logic, 155(1):16–31, 2008

Reference 33

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Observation 687f22e6-7240-4d0b-91a1-a0c0da37ff8d · outbound

This paper cites Lecture Notes in Logic.

Some applications of the real strict order property hierarchy Lecture Notes in Logic

Reference 34

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Observation 70cb614b-97d0-4666-a4a4-bcbd51cc7052 · outbound

This paper cites On amalgamation in NTP 2 theories and generically simple generics.Notre Dame Journal of Formal Logic, 61(2):233 – 243, 2020.

Some applications of the real strict order property hierarchy On amalgamation in NTP 2 theories and generically simple generics.Notre Dame Journal of Formal Logic, 61(2):233 – 243, 2020

Reference 35

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Observation 160eced4-5e70-416d-afd7-e2cc75f47ce2 · outbound

This paper cites An independence theorem forNTP 2 theories.The Journal of Symbolic Logic, 79(1):135–153, 2014.

Some applications of the real strict order property hierarchy An independence theorem forNTP 2 theories.The Journal of Symbolic Logic, 79(1):135–153, 2014

Reference 36

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Pith citing papers

Observation 3265c118-244e-40f9-9466-81f616152755 · inbound

SOP$_2$=SOP$_3$ cites this paper.

SOP$_2$=SOP$_3$ Some applications of the real strict order property hierarchy

Reference 23

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source=pdf_text observed=2026-08-14T14:42:44.054549Z digest=sha256:bed69932426a06770a4b0c33fa7ad1d733896b87af731258409ebd98f689ae43