Description

Book Synopsis

This is the second of two volumes by Professor Cherlin presenting the state of the art in the classification of homogeneous structures in binary languages and related problems in the intersection of model theory and combinatorics. Researchers and graduate students in the area will find in these volumes many far-reaching results and interesting new research directions to pursue. This volume continues the analysis of the first volume to 3-multi-graphs and 3-multi-tournaments, expansions of graphs and tournaments by the addition of a further binary relation. The opening chapter provides an overview of the volume, outlining the relevant results and conjectures. The author applies and extends the results of Volume I to obtain a detailed catalogue of such structures and a second classification conjecture. The book ends with an appendix exploring recent advances and open problems in the theory of homogeneous structures and related subjects.

Table of Contents

18. Classification problems for small binary languages; 19. Homogeneous 3-multi-graphs; 20. Imprimitive homogeneous 2-multi-tournaments; 21. 3-constrained homogeneous 2-multi-tournaments; 22. Homogeneous 2-multi-tournaments: forbidden triangles; Conclusion; Appendix B. Open problems and some recent results; References for Volume II; Index.

Homogeneous Ordered Graphs Metrically Homogeneous Graphs and Beyond

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    A Hardback by Gregory Cherlin

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      Book details

      Publisher Cambridge University Press
      Published 7 July 2022
      ISBN-13 9781009229487
      978-1009229487
      ISBN-10 1009229486
      Also in:
      Mathematical logic

      Description

      Book Synopsis

      This is the second of two volumes by Professor Cherlin presenting the state of the art in the classification of homogeneous structures in binary languages and related problems in the intersection of model theory and combinatorics. Researchers and graduate students in the area will find in these volumes many far-reaching results and interesting new research directions to pursue. This volume continues the analysis of the first volume to 3-multi-graphs and 3-multi-tournaments, expansions of graphs and tournaments by the addition of a further binary relation. The opening chapter provides an overview of the volume, outlining the relevant results and conjectures. The author applies and extends the results of Volume I to obtain a detailed catalogue of such structures and a second classification conjecture. The book ends with an appendix exploring recent advances and open problems in the theory of homogeneous structures and related subjects.

      Table of Contents

      18. Classification problems for small binary languages; 19. Homogeneous 3-multi-graphs; 20. Imprimitive homogeneous 2-multi-tournaments; 21. 3-constrained homogeneous 2-multi-tournaments; 22. Homogeneous 2-multi-tournaments: forbidden triangles; Conclusion; Appendix B. Open problems and some recent results; References for Volume II; Index.

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