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
Denis I. Saveliev, A note on restriction rules, 2023 , 20 pp., arXiv: 2312.06626
2022
2.
D. I. Saveliev, “On reduction and separation of projective sets in Tychonoff spaces”, Russian Math. Surveys, 77:1 (2022), 180–182
3.
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
2020
4.
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, Hausdorff operations and the reduction and separation properties in Tychonoff spaces, 2020 , arXiv: 2001.02033
6.
Denis I. Saveliev, On two types of ultrafilter extensions of binary relations, 2020 , arXiv: 2001.02456
2019
7.
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, Hindman finite sums theorem and its application to topologizations of algebras, 2018 , 20 pp., prinyata v Zapiski nauchnykh seminarov POMI, arXiv: 1810.01947
9.
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, “On Zariski topologies on polyrings”, Russian Math. Surveys, 72:4 (2017), 770–772
11.
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
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
2012
18.
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
19.
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
2011
20.
D. I. Saveliev, “Ultrafilter extensions of models”, Logic and Its Applications, Lecture Notes in Computer Science, Springer, 2011, 162–177
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