Geodesic
A note on pseudofinite acyclic graphs
The Bulletin of Irkutsk State University. Series Mathematics, Tome 50 (2024), pp. 116-124 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Acyclic graphs approximated by finite acyclic graphs are considered. It is proved that any countably categorical acyclic graph is smoothly approximable. An example of pseudofinite acyclic graph theory is given, which has an even, odd, and infinite number of rays.
Keywords: approximation of theory, tree, acyclic graph, pseudofinite theory, smoothly approximated structure
Mots-clés : pseudofinite graph. 
@article{IIGUM_2024_50_a7,
     author = {N. D. Markhabatov and Y. R. Baissalov},
     title = {A note on pseudofinite acyclic graphs},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {116--124},
     year = {2024},
     volume = {50},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2024_50_a7/}
}
TY  - JOUR
AU  - N. D. Markhabatov
AU  - Y. R. Baissalov
TI  - A note on pseudofinite acyclic graphs
JO  - The Bulletin of Irkutsk State University. Series Mathematics
PY  - 2024
SP  - 116
EP  - 124
VL  - 50
UR  - http://geodesic.mathdoc.fr/item/IIGUM_2024_50_a7/
LA  - en
ID  - IIGUM_2024_50_a7
ER  - 
%0 Journal Article
%A N. D. Markhabatov
%A Y. R. Baissalov
%T A note on pseudofinite acyclic graphs
%J The Bulletin of Irkutsk State University. Series Mathematics
%D 2024
%P 116-124
%V 50
%U http://geodesic.mathdoc.fr/item/IIGUM_2024_50_a7/
%G en
%F IIGUM_2024_50_a7
N. D. Markhabatov; Y. R. Baissalov. A note on pseudofinite acyclic graphs. The Bulletin of Irkutsk State University. Series Mathematics, Tome 50 (2024), pp. 116-124. http://geodesic.mathdoc.fr/item/IIGUM_2024_50_a7/

[1] Garcia D., Robles M., Pseudofiniteness and measurability of the everywhere infinite forest, 2023, arXiv: 2309.00991 | DOI

[2] Grinberg D., An introduction to graph theory, 2023, arXiv: 2308.04512 | DOI

[3] Herre Heinrich, Mekler Allan, Smith Kenneth, “Superstable graphs”, Fundamenta Mathematicae, 118:2 (1983), 75–79 | DOI | MR | Zbl

[4] Ivanov A., “The structure of superflat graphs”, Fundamenta Mathematicae, 143:2 (1993), 107–117 | DOI | MR | Zbl

[5] Kantor W.M., Liebeck M.W., Macpherson H.D., “$\aleph_0$-categorical structures smoothly approximated by finite substructures”, Proc. London Math. Soc., 59 (1989), 439–463 | DOI | MR | Zbl

[6] Malyshev S. B., The Bulletin of Irkutsk State University. Series Mathematics, 46 (2023), 110–120 | DOI | Zbl

[7] Marker D., Model Theory: An Introduction, Graduate Texts in Mathematics, 271, Springer Verlag Publ., New York–Berlin–Heidelberg, 2002, 342 pp. | MR

[8] Markhabatov N. D., “Approximations of Acyclic Graphs”, The Bulletin of Irkutsk StateUniversity. Series Mathematics, 40 (2022), 104–111 | DOI | MR | Zbl

[9] Markhabatov N. D., Sudoplatov S. V., “Approximations of Regular Graphs”, Herald of the Kazakh-British Technical University, 19:1 (2022), 44–49 | DOI

[10] Myasnikov A.G., Remeslennikov V.N., “Generic Theories as a Method for Approximating Elementary Theories”, Algebra and Logic, 53 (2015), 512–519 | DOI | MR | Zbl

[11] Nurtazin A.T., “Graphs and Models with finite chains”, Siberian Electronic Mathematical Reports, 4 (2007), 238–248 | MR | Zbl

[12] Ovchinnikova E.V., Shishmarev Yu.E., “Countably categorical graphs”, Ninth All-Union Conference on Mathematical Logic, dedicated to the 85th anniversary of Corresponding Member of the USSR Academy of Sciences A.A. Markov (Leningrad, September 27-29, 1988), 1988, 120 | MR

[13] Podewski Klaus-Peter, and Ziegler Martin, “Stable graphs”, Fundamenta Mathematicae, 100:2 (1978), 101–107 | DOI | MR | Zbl

[14] Sudoplatov S. V., “Approximations of theories”, Siberian Electronic Mathematical Reports, 17 (2020), 715–725 | MR | Zbl

[15] Tao T., “Expanding polynomials over finite fields of large characteristic, and a regularity lemma for definable sets”, Contributions to Discrete Mathematics, 10:1 (2014), 22–98 | MR

[16] Valizadeh A.N., Pourmahdian M., “Pseudofiniteness in Hrushovski Constructions”, Notre Dame J. Formal Log., 61 (2020), 1–10 | DOI | MR | Zbl

[17] Valizadeh A.N., Pourmahdian M., “Strict Superstablity and Decidability of Certain Generic Graphs”, Bull. Iran. Math. Soc., 45 (2019), 1839–1854 | DOI | MR | Zbl

[18] Woodrow R.E., Theories with a finite number of countable models and a small language, Ph. D. Thesis, Simon Fraser University, 1976, 99 pp. | MR