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Details of project

 
Identifier
83726
Type K
Principal investigator Juhász, István
Title in Hungarian Halmazelméleti topológia
Title in English Set-theoretic topology
Keywords in Hungarian halmazelmélet, topologikus terek, számosságfüggvények
Keywords in English set-theory, topological spaces, cardinal functions
Discipline
Mathematics (Council of Physical Sciences)100 %
Ortelius classification: Set theory
Panel Mathematics and Computing Science
Department or equivalent Alfréd Rényi Institute of Mathematics
Participants Elekes, Márton
Farkas, Barnabás
Gyenis, Zalán
Hajnal, András
Sági, Gábor
Soukup, Lajos
Szentmiklóssy, Zoltán
Vizer, Máté
Starting date 2011-02-01
Closing date 2015-01-31
Funding (in million HUF) 17.595
FTE (full time equivalent) 10.52
state closed project
Summary in Hungarian
A 60-as évek második fele óta folyamatos és intenzív kutatómunka folyik Hajnal András és Juhász István vezetésével Budapesten a halmazelméleti topológia területén. Ennek a munkának nemzetközi elismertségét bizonyítja pl. az a tény, hogy a témában 2003-ban Budapesten megrendezett konferencián olyan világhírű tudósok vettek részt, mint A. V. Arhangelszkij, A. Dow, K. Kunen, J. van Mill és S. Shelah. Pályázatunknak éppen az a célja, hogy ezeket a sikeres kutatásokat tovább folytassuk, természetesen kitejesztve őket új irányokba is, mint pl. a leíró halmazelmélet, valós függvénytan és mértékelmélet. A pályázat elnyerése lehetővé tenné számunkra, hogy kiterjedt nemzetközi kapcsolatainkat fenntartsuk, sőt a lehetőségekhez mérten kibővitsük, továbbá hogy az eredményes kutatások folytatásához szükséges technikai és egyéb feltéteteleket biztosítsuk.
Summary
Since the second half of the sixties an intensive and uninterrupted
research work has been carried out by our group in Budapest in the
area of set-theoretic topology, under the leadership of András
Hajnal and István Juhász. The international recognition of this work
is well-demonstrated by the fact that the conference that was
organized in this area in Budapest in 2003 was attended by such
scientists of international fame as A. V. Arhangelszkij, A. Dow, K.
Kunen, J. van Mill and S. Shelah. The exact aim of this project is
to carry on this successful research work and, of course, extend it
to new directions like descriptive set-theory, theory of real
functions, and measure-theory.

Getting this grant would enable us to keep up, and possibly even
extend, our wide ranging international relations in the area of
set-theoretic topology. Also, it would make it possible for us to
insure the technical and other types of conditions necessary for
carrying on our successful research work.





 

Final report

 
Results in Hungarian
Ebben az OTKA-pályázatban -- kutatási tervünknek megfelelően -- kutatásokat végeztünk és jelentős eredményeket értünk el a következő négy területen: (I) Halmazelméleti topológia (II) Leíró halmazelmélet (III) Valós analízis és mértékelmélet . (IV) Végtelen és véges kombinatorika (V) Modell-elmélet és matematika filozófiája Eredményeinket 40 dolgozatban írtuk le, amelyek túlnyomó többsége a megfelelő terület legrangosabb nemzetközi folyóirataiban jelentek meg, illetve fognak megjelenni . Ezek közül 6 dolgozatot már benyujtottunk,de eddig még nem lettek elfogadva. Kutatócsoportunk a vezető kutató mellett 8 résztvevő kutatóból és 2 PhD-hallgatóból állt. Utóbbiak egyike a PhD fokozatot 2013-ban megszerezte, míg a másik hamarosan végezni fog. Mindketten lényegesen járultak hozzá az eredményeinkhez. Kutatási eredményeinkről számos nemzetközi konferencián is számot adtunk, közülünk négyen (Elekes, Juhász, Sági, Soukup) több jelentős konferencián mint plenáris és/vagy meghívott előadó.
Results in English
In the present project, following our research plan, we have done research and established a number of significant results in the following five areas: I. Set-theoretic topology II. Descriptive set theory III. Real analysis and measure theory IV. Combinatorics V. Model theory and philosophy of mathematics Our research group consisted of the PI and 8 more researchers, moreover 2 PhD students. One of the students has received his degree in 2013 and is now a postdoc with us and the other is finishing momentarily. Both of them have contributed significantly to our results. Our results were presented in 40 publications, almost all of which appeared or will appear in the leading international journals of these fields. 6 of these papers have been submitted but not accepted as yet. The members of our group participated at a large number of international conferences, four of us (Elekes, Juhász, Sá}gi, and Soukup) as plenary and/or invited speakers at many of these.
Full text https://www.otka-palyazat.hu/download.php?type=zarobeszamolo&projektid=83726
Decision
Yes





 

List of publications

 
Erdős P L; Miklosi I; Soukup L:: Towards random uniform sampling of bipartite graphs with given degree sequence, The Electronic Journal of Combinatorics, 20, 2013
Gyenis Z; Rédei M:: Why Bertrand's Paradox is not paradoxical but is felt so?, Recent Developments in the Philosophy of Science: EPSA13 Helsinki, U. Maki, S. Ruphy, G. Schurz, I. Votsis, (eds.) (Springer, forthcoming), 2015
Elekes M; Keleti T:: Decomposing the real line into Borel sets closed under addition, Math. Logic Quaterly, to appear, 2015
Elekes M; Vidnyánszky Z:: Characterization of order types of pointwise linearly ordered families of Baire class 1 functions, Advances in Math., submitted, 2014
Balka R; U B Darji; Elekes M:: Hausdorff and packing dimension of fibers and graphs of prevalent continuous maps, Advances in Math., submitted, 2014
Elekes M, Kiss V, Vidnyánszky Z: Ranks on the Baire class $\xi$ functions, Trans. Amer. Math. Soc., submitted, 2014
Kim Y; Kumbhat M; Nagy Z L; Patkos B; Pokrovskiy A; Vizer M:: Identifying codes and searching with balls in graphs, Discrete Applied Mathematics, to appear, 2015
Füredi Z; Gerbner D; Vizer M:: A discrete isodiametric result: the Erdős-Ko-Rado theorem for multisets, European Journal of Combinatorics, to appear, 2015
Sagi G:: On nonrepresentable G-polyadic algebras with representable cylindric reducts, Log. J. IGPL 19 (2011), no. 1, pp. 105-109, 2011
Sagi, G; Sziraki D:: Some variants of Vaught's conjecture from the perspective of algebraic logic, Log. J. IGPL 20 (2012), no. 6, pp. 1064-1082, 2012
Sagi G:: Polyadic algebras, Cylindric-like algebras and algebraic logic, (ed.s: H. Andreka, M. Ferenczi, I. Nemeti), pp. 367-389, Bolyai Soc. Math. Stud., 22, János Bolyai Math. Soc., Budapest, 2012, 2012
Balka R; Buczolich Z; Elekes M: A new fractal dimension: The topological Hausdorff dimension, Advances in Math., to appear, 2014
Elekes M; Steprans J: Haar null sets and the consistent reflection of non-meagreness, Canad. J. Math., 66 (2014), 303 - 322., 2014
Soukup D; Soukup L; Spadaro S: Comparing weak versions of separability (title has changed), Top. Appl., Vol 160,pp 2538-2566, 2013
Soukup L: Essentially disjoint families, conflct free colorings, and Shelah's Revised GCH, Acta Math Hung, Vol140, Issue 3, pp 293-303, 2013
Balka R; Elekes M; Máthé A: Answer to a question of Kolmogorov, Proc. Amer. Math. Soc., to appear, 2014
Juhász I; Shelah S;: Strong colorings yield discretely untouchable points in $\omega$-bounded spaces, Proc. Amer. Math. Soc. (to appear), 2015
Juhász I; Soukup L; Szentmiklóssy Z:: Regular spaces of small extent are $\omega$-resolvable, Fund. Math. 228 (2015), pp. 27 - 46., 2015
Soukup D; Soukup L:: Partitioning bases of topological spaces, CMUC 55 , issue 4, pp. 537-566, 2014
Patkós B; Vizer M:: Game saturation of intersecting families, Central European Journal of Mathematics 12 (2014), no. 9, pp. 1382-1389, 2014
Balka R; Darji U B; Elekes M:: Bruckner-Garg-type results with respect to Haar null sets in C[0,1], Proc. Edinb. Math. Soc., to appear, 2013
Elekes M; Vidnyánszky Z:: Haar null sets without $G_\delta$ hulls, Israel J. Math. , to appear, 2014
Goldstern M; Sági G; . Shelah S:: Very many clones above the unary clone, Algebra Universalis 69 (2013), no. 4, 387-399, 2013
Gyenis Z; Sági G:: Upward Morley's theorem downward, Math. Log. Q. 59 (2013), no. 4-5, 303-331, 2013
Gyenis Z:: Interpolation property and homogeneous structures, Logic Journal of IGPL, 22 (2014), pp. 597-607., 2014
Gyenis Z; Rédei M:: Can Bayesian agents always be rational? A principled analysis of consistency of an Abstract Principal Principle, Philosophy of Science, submitted, 2014
Borodulin-Nadzieja P; Farkas B; Plebanek G:: Representations of ideals in Polish groups and in Banach spaces, J. Symbolic Logic (to appear), 2014
Elekes M; Soukup D; Soukup L; Szentmiklóssy Z:: Decompositions of edge-colored infinite complete graphs into monochromatic paths, Combinatorica (submitted), 2015
Juhász I; Soukup L; Szentmiklóssy Z:: Between countably compact and $\omega$-bounded, Top. Appl., to appear, 2015
Balka R; Darji U B; Elekes M:: Bruckner-Garg-type results with respect to Haar null sets in C[0,1], Proc. Edinb. Math. Soc. (submitted), 2014
Elekes M; Vidnyánszky Z:: Haar null sets without $G_\delta$ hulls, Israel J. Math. (submitted), 2014
Goldstern M; Sági G; . Shelah S:: Very many clones above the unary clone, Algebra Universalis 69 (2013), no. 4, 387-399, 2013
Gyenis Z; Sági G:: Upward Morley's theorem downward, Math. Log. Q. 59 (2013), no. 4-5, 303-331, 2013
Sági G:: Designing Decidable Logics of Epistemology, Proceedings of the 12th International Conference on Informatics, (ed.s: Valerie Novitzka, Stefan Hudak), pp. 225-227, Spisska Nova Ves, Slovakia., 2013
Gyenis Z:: Interpolation property and homogeneous structures, Logic Journal of IGPL, to appear, 2013
Gyenis Z; Rédei M:: Can Bayesian agents always be rational? A principled analysis of consistency of an Abstract Principal Principle, Philosophy of Science, 2014
Borodulin-Nadzieja P; Farkas B:: Representations of ideals in Polish groups and in Banach spaces, J. Symbolic Logic (submitted), 2014
Elekes M; Soukup D; Soukup L; Szentmiklóssy Z:: Monochromatic path decompositions of in nite complete graphs, ***, 2014
Juhász I; Soukup L; Szentmiklóssy Z:: Between countably compact and $\omega$-bounded, ***, 2014
Juhász I; Shelah S;: Strong colorings yield discretely untouchable points in $\omega$-bounded spaces, Proc. Amer. Math. Soc. (to appear), 2013
Juhász I; Soukup L; Szentmiklóssy Z:: Regular spaces of small extent are $\omega$-resolvable, Fund. Math. (submitted), 2014
Soukup D; Soukup L:: Partitioning bases of topological spaces, CMUC, 2014
Patkós B; Vizer M:: Game saturation of intersecting families, Central European Journal of Mathematics, to appear, 2014
Juhász I; van Mill J; Weiss W: Variations on $\omega$-boundedness, Israel J. Math., to appear, 2012
Balka R; Buczolich Z; Elekes M: A new fractal dimension: The topological Hausdorff dimension, J. Amer. Math. Soc., submitted, 2012
Elekes M: A covering theorem and the random-indestructibility of the density zero ideal, Real Anal. Exchange 37 (2011), no. 1, 55-60., 2011
Elekes M; Steprans J: Haar null sets and the consistent reflection of non-meagreness, Canad. J. Math., accepted, 2012
Balka R; Elekes M: Continuous horizontally rigid functions of two variables are affine, Aequationes Math. 84 (2012), no. 1-2, 27-39., 2012
Elekes M; Keleti T; Máthé A: Reconstructing geometric objects from the measures of their intersections with test sets,, J. Fourier Anal. Appl., accepted, 2012
Balka R; Buczolich Z; Elekes M: Topological Hausdorff dimension and level sets of generic continuous functions on fractals, Chaos Solitons Fractals 45 (2012), 1579-1589., 2012
Soukup D; Soukup L; Spadaro S: Comparing weak versions of separability (title has changed), Top. Appl., submitted, 2012
Goldstern M; Sági G; Shelah: Clones above the unary clone, Algebra Universalis, to appear, 2012
Gyenis Z; Sági G: Upward Morley's Theorem Downward, Math. Logic Quarterly, to appear, 2013
Sági G: Vaught's conjecture from the perspective of algebraic logic, submitted, Math. Logic Quarterly, submitted, 2012
Borodulin-Nadzieja P; Farkas B: Cardinal coefficients associated to certain orders on ideals, Archive for Mathematical Logic, to appear, 2012
Balcerzak M; Farkas B; Glab S: Covering properties of ideals, Arch. Math. Logic, to appear, 2012
Juhász I; van Mill J:: Can a free ultrafilter be connectedly generated?, Questions and Answers in General Topology 30 (2012), pp. 103--104., 2012
Soukup L: Essentially disjoint families, conflct free colorings, and Shelah's Revised GCH, Acta Math Hung, to appear, 2013
Fuchino S; Sakai H; Soukup L; Usuba T: More about the Fodor-type Reflection Principle, Fund. Math., submitted, 2013
Juhász I; Soukup L; Szentmiklóssy Z; Weiss W: Lifting some properties of compacta to Lindelöf P-spaces, preprint, 2013
Soukup D; Soukup L: Partitioning bases of topological spaces, preprint, 2013
Balka R; Elekes M; Máthé A: Answer to a question of Kolmogorov, Proc. Amer. Math. Soc., submitted, 2013
Juhász I; van Mill J; Weiss W: Variations on $\omega$-boundedness, Israel J. Math., 194 (2013), no. 2, pp. 745-766., 2013
Elekes M; Keleti T; Máthé A: Reconstructing geometric objects from the measures of their intersections with test sets,, J. Fourier Anal. Appl., 19 (2013), no. 3, 545-576, 2013
Juhász I; Szentmiklóssy Z: Compacta are maximally $G_\delta$-resolvable, CMUC 54, 2 (2013), pp. 259 –261., 2013
Balka R; Elekes M; Máthé A: Answer to a question of Kolmogorov, Proc. Amer. Math. Soc., to appear, 2014




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