38 research outputs found
HalmazelmĂ©let; PartĂciĂł kalkulus, VĂ©gtelen gráfok elmĂ©lete = Set Theory; Partition Calculus , Theory of Infinite Graphs
ElĹ‘zetes tervĂĽnknek megfelelĹ‘en a halmazelmĂ©let alábbi terĂĽletein vĂ©geztĂĽnk kutatást Ă©s Ă©rtĂĽnk el számos eredmĂ©nyt: I. Kombinatorika II. A valĂłsak számsosságinvariánsai Ă©s ideálelmĂ©let III. HalmazelmĂ©leti topolĂłgia Ezek mellett Sági Gábor kiterjedt kutatást vĂ©gzett a modellelmĂ©let terĂĽletĂ©n , amely eredmĂ©nyek kapcsolĂłdnak a kombinatorikához is. EredmĂ©nyeinket 38 közlemĂ©nyben publikáltuk, amelyek majdnem mind az adott terĂĽlet vezetĹ‘ nemzetközi lapjaiban jelentel meg (5 cikket csak benyĂşjtottunk). Számos nemzetközi konferencián is rĂ©sztvettĂĽnk, Ă©s hárman közűlĂĽnk (Juhász, Sádi, Soukup) plenáris/meghĂvott elĹ‘adĂłk voltak számos alkalommal. | Following our research plan, we have mainly done research -- and established a number of significant results -- in several areas of set theory: I. Combinatorics II. Cardinal invariants of the continuum and ideal theory III. Set-theoretic topology In addition to these, G. Sági has done extended research in model theory that had ramifications to combinatorics. We presented our results in 38 publications, almost all of which appeared or will appear in the leading international journals of these fields (5 of these papers have been submitted but not accepted as yet). We also participated at a number of international conferences, three of us (Juhász, Sági, Soukup) as plenary and/or invited speakers at many of these
Universal graphs with forbidden subgraphs and algebraic closure
We apply model theoretic methods to the problem of existence of countable
universal graphs with finitely many forbidden connected subgraphs. We show that
to a large extent the question reduces to one of local finiteness of an
associated''algebraic closure'' operator. The main applications are new
examples of universal graphs with forbidden subgraphs and simplified treatments
of some previously known cases
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Set Theory
This workshop included selected talks on pure set theory and its applications, simultaneously showing diversity and coherence of the subject
Recommended from our members
Set Theory
This stimulating workshop exposed some of the most exciting recent develops in set theory, including major new results about the proper forcing axiom, stationary reflection, gaps in P(ω)/Fin, iterated forcing, the tree property, ideals and colouring numbers, as well as important new applications of set theory to C*-algebras, Ramsey theory, measure theory, representation theory, group theory and Banach spaces