01.01.06 (Mathematical logic, algebra, and number theory)
E-mail:
Keywords:
models of set theory,
axiom of choice,
cardinal arithmetic,
cardinals without choice,
axiom of regularity and non-well-founded sets,
ultrafilters and ultra-extensions of models,
general topology.
Subject:
set theory, model theory, mathematical logic, general topology
Main publications:
Denis I. Saveliev, “A game on the universe of sets”, Izvestiya: Mathematics, 72:3 (2008), 581–625
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
D. I. Saveliev, “On reduction and separation of projective sets in Tychonoff spaces”, Russian Math. Surveys, 77:1 (2022), 180–182
2.
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
3.
Denis I. Saveliev, Ilya B. Shapirovsky, “On modal logics of model-theoretic relations”, Studia Logica, 108 (2020), 989-1017 , arXiv: 1804.09810
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
D. I. Saveliev, “On Zariski topologies on polyrings”, Russian Math. Surveys, 72:4 (2017), 770–772
6.
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
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, “On idempotents in compact left topological universal algebras”, Topology Proceedings, 43 (2014), 37–46
12.
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
13.
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
14.
D. I. Saveliev, “Ultrafilter extensions of models”, Logic and Its Applications, Lecture Notes in Computer Science, Springer, 2011, 162–177
D. I. Saveliev, “A game on the universe of sets”, Izv. Math., 72:3 (2008), 581–625
16.
D. I. Saveliev, “A Report on a Game on the Universe of Sets”, Math. Notes, 81:5 (2007), 716–719
17.
D. I. Saveliev, “On Isomorphisms of Relations Embedded into Each Other”, Math. Notes, 74:4 (2003), 543–556
18.
D. I. Saveliev, “A remark on the connection between linear order and measure and category”, Russian Math. Surveys, 53:6 (1998), 1365–1366
ArXiv
19.
Denis I. Saveliev, A note on restriction rules, 2023 , 20 pp., arXiv: 2312.06626
20.
Denis I. Saveliev, Hausdorff operations and the reduction and separation properties in Tychonoff spaces, 2020 , arXiv: 2001.02033
21.
Denis I. Saveliev, On two types of ultrafilter extensions of binary relations, 2020 , arXiv: 2001.02456
22.
D. I. Saveliev, Hindman finite sums theorem and its application to topologizations of algebras, 2018 , 20 pp., prinyata v Zapiski nauchnykh seminarov POMI, arXiv: 1810.01947
23.
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
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
On Ultralter Extensions of First-Order Models D. I. Saveliev The joint seminar of the Sector 4.1 (IITP RAS) and Poncelet French-Russian laboratory "Arithmetic Geometry and Coding Theory" February 25, 2014 17:30
Contact us: