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Well-Quasi-Ordering, The Tree Theorem, and Vazsonyi's Conjecture
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This paper presents an expanded version of part of my doctoral dissertation at Princeton University. I wish to express my gratitude for the encouragement and direction of R
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Let à be a set of P-characteristic atoms. Then ¢*ca is a well-quasi relation on Ã.
“Proposition 4.4.11.Let à be a set of P -characteristic atoms.Then ¢ * ca is a well-quasi relation on Ã.”
From Controlling generalization and polyvariance in partial deduction of normal logic programs (1998) · cites this paper as Kruskal [1960]
Section 2 defines well-quasi-ordering, and the paper discusses well-quasi-ordered tree spaces, but these passages do not address P-characteristic atoms or the relation ¢*ca. Searches for “P-characteristic atoms” and the claimed relation found no passage establishing that proposition; page numbers were not available in our copy. (LLM, conf=0.72)
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Research works printed but not linked: 5
- Higman, Graham, 1952, Ordering by divisibility in abstract algebras, Proc. London Math. Soc. (3), 2, 326, 10.1112/plms/s3-2.1.326 · DOI · Paper page
- Joseph Kruskal, Well-partial-order and Rado’s conjecture, submitted to the Proc. London Math. Soc.
- \bysame, The theory of well-partially-ordered sets, June, 1954, Princeton University, doctoral thesis.
- Neumann, B. H., 1949, On ordered division rings, Trans. Amer. Math. Soc., 66, 202, 10.2307/1990552 · DOI
- Rado, R., 1954, Partial well-ordering of sets of vectors, Mathematika, 1, 89, 10.1112/S0025579300000565 · DOI
Cited by
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Controlling generalization and polyvariance in partial deduction of normal logic programs
Leuschel, M., Martens, B., & De Schreye, D. (1998) · ACM Transactions on Programming Languages and Systems · doi:10.1145/271510.271525 · Cited by 88
Metadata
- Authors
- Kruskal, J. B.
- Corresponding author
- Kruskal, J. B.
- Venue
- Transactions of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Published
- 1960
- Volume
- 95
- Issue
- 2
- Pages
- 210-225
- ISSN
- 0002-9947 (ISSN-L)
- 1088-6850
- OpenAlex
- W2018765574
- Cited by
- 497
- References
- 0
- Citations by year
- 2026: 3 · 2025: 3 · 2024: 3 · 2023: 9 · 2022: 6 · 2021: 27 · 2020: 19 · 2019: 18 · 2018: 6 · 2017: 14 · 2016: 11 · 2015: 8 · 2014: 11 · 2013: 14 · 2012: 17
- FWCI
- 0.74
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Transactions of the American Mathematical Society (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Geometry and Topology › Advanced Topology and Set Theory
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Advanced Combinatorial Mathematics
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Limits and Structures in Graph Theory
- Keywords
- well-quasi-ordering, infinite combinatorics, trees, set theory
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