01.01.06 (математическая логика, алгебра и теория чисел)
E-mail:
Ключевые слова:
модели теории множеств,
аксиома выбора,
кардинальная арифметика,
кардиналы без аксиомы выбора,
аксиома регулярности и нефундированные множества,
ультрафильтры и ультрарасширения моделей, общая топология.
Основные темы научной работы
теория множеств, теория моделей, математическая логика, общая топология
Основные публикации:
Д.И. Савельев, “Игра на универсуме множеств”, Известия РАН, сер. матем., 72:3 (2008), 175–224
Denis I. Saveliev, “On ultrafilter extensions of models”, The Infinity Project Proceedings, S.D. Friedman et al. (eds.), CRM Documents, 11, Barcelona, 2012, 599–616
Denis I. Saveliev, “On idempotents in compact left topological universal algebras”, Topology Proceedings, 43 (2014), 37–46
Denis I. Saveliev, “Ultrafilter extensions of linearly ordered sets”, Order, 32:1 (2015), 29–41
Paul Howard, Denis I. Saveliev, Eleftherios Tachtsis, “On the set-theoretic strength of the existence of disjoint cofinal sets in posets without maximal elements”, Mathematical Logic Quarterly, 62:3 (2016), 155–176
N. L. Poliakov, D. I. Saveliev, On ultrafilter extensions of first-order models and ultrafilter interpretations, 2018 , Archive for Mathematical Logic 60 (2021), 625–681, arXiv: 1812.06248
P. E. Howard, D. I. Saveliev, E. Tachtsis, “On the set-theoretic strength of the existence of disjoint cofinal sets in posets without maximal elements”, Mathematical Logic Quarterly, 62:3 (2016), 155–176
D. I. Saveliev, S. Shelah, Ultrafilter extensions do not preserve elementary equivalence, Paper 1132 in Shelahs list, 2017 , Mathematical Logic Quarterly, 65:4 (2019), 511–515, arXiv: 1712.06198
N. L. Poliakov, D. I. Saveliev, “On two concepts of ultrafilter extensions of first-order models and their generalizations”, Logic, Language, Information, and Computation, 24th International Workshop on Logic, Language, Information, and Computation (WoLLIC) (18-21.07 2017, London), Lecture Notes in Comput. Sci., 10388, eds. J. Kennedy, R. J. G. B. de Queiroz, Springer, Berlin, Heidelberg, 2017, 336–348
Denis I. Saveliev, “On first-order expressibility of satisfiability in submodels”, WoLLIC 2019, Lecture Notes in Computer Science, 11541, eds. R. Iemhoff et al., Springer-Verlag, 2019, 584–593 arXiv: 1903.04993
Д. И. Савельев, “Сообщение об игре на универсуме множеств”, Матем. заметки, 81:5 (2007), 797–800; D. I. Saveliev, “A Report on a Game on the Universe of Sets”, Math. Notes, 81:5 (2007), 716–719
N. L. Poliakov, D. I. Saveliev, “Generalizations of the Rudin–Keisler preorder and their model-theoretic applications”, Bulletin of L.N. Gumilyov Eurasian National University. Mathematics, computer science,mechanics series, 151:2 (2025), 6–11
11.
Denis I. Saveliev, A note on restriction rules, 2023 , 20 pp., arXiv: 2312.06626
12.
Д. И. Савельев, “О редукции и отделимости проективных множеств в тихоновских пространствах”, УМН, 77:1(463) (2022), 189–190; D. I. Saveliev, “On reduction and separation of projective sets in Tychonoff spaces”, Russian Math. Surveys, 77:1 (2022), 180–182
13.
Denis I. Saveliev, Ilya B. Shapirovsky, “Medvedev’s logic and products of converse well orders”, Advances in Modal Logic, 14, College Publications, 2022, 681–696
14.
Denis I. Saveliev, Hausdorff operations and the reduction and separation properties in Tychonoff spaces, 2020 , arXiv: 2001.02033
15.
Denis I. Saveliev, On two types of ultrafilter extensions of binary relations, 2020 , arXiv: 2001.02456
16.
D. I. Saveliev, Hindman finite sums theorem and its application to topologizations of algebras, 2018 , 20 с., принята в Записки научных семинаров ПОМИ, arXiv: 1810.01947
17.
Д. И. Савельев, “О топологиях Зариского на поликольцах”, УМН, 72:4(436) (2017), 195–196; D. I. Saveliev, “On Zariski topologies on polyrings”, Russian Math. Surveys, 72:4 (2017), 770–772
18.
Д. И. Савельев, “Замечание о сингулярных кардиналах без аксиомы выбора”, УМН, 71:2(428) (2016), 213–214; D. I. Saveliev, “A note on singular cardinals without the axiom of choice”, Russian Math. Surveys, 71:2 (2016), 385–387
19.
D. I. Saveliev, I. B. Shapirovsky, “On modal logic of submodels”, 11th Advances in Modal Logic, Short Papers, 2016, 115–119
20.
D. I. Saveliev, “On idempotents in compact left topological universal algebras”, Topology Proceedings, 43 (2014), 37–46
21.
D. I. Saveliev, “On ultrafilter extensions of models”, The Infinity Project Proceedings, CRM Documents, 11, eds. S.-D. Friedman et al., CRMS, Barcelona, 2012, 599–616http://folk.uio.no/larsk/Documents_11-2.pdf
22.
D. I. Saveliev, “On modal logic of dynamics: actions of arbitrary semigroups”, 9th Advances in Modal Logic, Short Presentations, eds. Th. Bolander et al., 2012, 68–75
23.
Д. И. Савельев, “Игра на универсуме множеств”, Изв. РАН. Сер. матем., 72:3 (2008), 175–224; D. I. Saveliev, “A game on the universe of sets”, Izv. Math., 72:3 (2008), 581–625
24.
Д. И. Савельев, “Об изоморфизме отношений, вкладывающихся друг в друга”, Матем. заметки, 74:4 (2003), 573–589; D. I. Saveliev, “On Isomorphisms of Relations Embedded into Each Other”, Math. Notes, 74:4 (2003), 543–556
25.
Д. И. Савельев, “Замечание о связи линейного порядка с мерой и категорией”, УМН, 53:6(324) (1998), 261–262; D. I. Saveliev, “A remark on the connection between linear order and measure and category”, Russian Math. Surveys, 53:6 (1998), 1365–1366
On Ultralter Extensions of First-Order Models Д. И. Савельев Совместный семинар лаборатории J.-V. Poncelet и сектора Алгебры и теории чисел № 4.1 ИППИ РАН «Арифметика, геометрия и теория кодирования» 25 февраля 2014 г. 17:30
