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
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 ultrafilter extensions of first-order models and ultrafilter interpretations, 2018 , Archive for Mathematical Logic 60 (2021), 625–681, arXiv: 1812.06248
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
D. I. Saveliev, “A Report on a Game on the Universe of Sets”, Math. Notes, 81:5 (2007), 716–719
10.
Denis I. Saveliev, A note on restriction rules, 2023 , 20 pp., arXiv: 2312.06626
11.
D. I. Saveliev, “On reduction and separation of projective sets in Tychonoff spaces”, Russian Math. Surveys, 77:1 (2022), 180–182
12.
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
13.
Denis I. Saveliev, Hausdorff operations and the reduction and separation properties in Tychonoff spaces, 2020 , arXiv: 2001.02033
14.
Denis I. Saveliev, On two types of ultrafilter extensions of binary relations, 2020 , arXiv: 2001.02456
15.
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
16.
D. I. Saveliev, “On Zariski topologies on polyrings”, Russian Math. Surveys, 72:4 (2017), 770–772
17.
D. I. Saveliev, “A note on singular cardinals without the axiom of choice”, Russian Math. Surveys, 71:2 (2016), 385–387
18.
D. I. Saveliev, I. B. Shapirovsky, “On modal logic of submodels”, 11th Advances in Modal Logic, Short Papers, 2016, 115–119
19.
D. I. Saveliev, “On idempotents in compact left topological universal algebras”, Topology Proceedings, 43 (2014), 37–46
20.
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
21.
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
22.
D. I. Saveliev, “A game on the universe of sets”, Izv. Math., 72:3 (2008), 581–625
23.
D. I. Saveliev, “On Isomorphisms of Relations Embedded into Each Other”, Math. Notes, 74:4 (2003), 543–556
24.
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 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
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