Gregory Cherlin. Preliminary Reports and Notes

Publications

Drafts

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1. Metrically homogeneous graphs of generic type I-III
Verification of the conjectured classification of the metrically homogeneous graphs, in three parts.
I. Triangle constraints and admissibility
II. Embedding theorem, base case.
III. Embedding theorem, inductive step.
2. Around the algebraicity problem in odd type (working title)
   Exposition of ideas of Burdges around analogs of L^*-theory for odd type groups of finite Morley rank.
   Draft expected late 2022.
   See also the next entry,
3. L*-Groups of odd type with restricted 2-toral automorphisms, I-IV with Jefffrey Burdges; drafts, 2022
   
   • I. High Prüfer 2-rank
   • II. Pruüfer 2-rank 2 and 2-rank at least 3: Component analysis
   • III. Identification of PSp4
   • IV. Toward the identification of G2
4. Universal graphs with one forbidden subgraph, the generic case, with S. Shelah
Constraints without trivial blocks (under development).
• Part I. Block paths with no trivial blocks. draft
• Part II. Reduction to block paths (in progress).

Notes

December, 2021
• Homogeneity and related topics: An extended bibliography, mainly through 2016
Includes a list sorted by topic.
Also found at arXiv:2111.15429 [math.LO], possibly less current.
Minor edits will be made here first. We do not intend to add many references later than 2016 but if we become aware of gaps prior to that date we will fill them.


November, 2020

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• Triangles in homogeneous 2-multi-tournaments: Case 1
Computations relating to triangle constraints in homogeneous 2-multi-tournaments.
Compare Monograph, Chapter 22.


September, 2013

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• Diameter 4
Fragmentary notes, broken off (121pp, Sep. 2013). Superseded by work in progress on the general case.

© G. Cherlin