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SUMMARY:Yatir Halevi (Technion - Israel Institute of Technology)
DTSTART:20251120T190000Z
DTEND:20251120T200000Z
DTSTAMP:20260423T035934Z
UID:OLS/189
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OLS/189/">Ar
 ound Taylor’s Conjecture and Model-Theoretic Tameness</a>\nby Yatir Hale
 vi (Technion - Israel Institute of Technology) as part of Online logic sem
 inar\n\n\nAbstract\nGiven a graph (G\, E)\, its chromatic number is the sm
 allest cardinal\n$\\kappa$ admitting a legal coloring of the vertices.\nTh
 e strong Taylor's conjecture states the following:\n\nIf  G is an infinite
  graph with chromatic number $\\geq \\aleph_1$\, then\nit contains all fin
 ite subgraphs of $Sh_n(\\omega)$ for some n\,\nwhere $Sh_n(\\omega)$ is th
 e n-shift graph (which we will introduce).\n\nThe conjecture was disproved
  by Hajnal and Komjáth\; however\, a variant\nof it still holds for $\\om
 ega$-stable\, superstable\, or stable graphs.\nOne can also restrict the c
 onjecture and ask when G contains all\nfinite subgraphs of the complete gr
 aph.\nWe give answers to this question when the edge relation of the graph
 \nis stable or when the graph itself is simple.\n\nJoint work with Itay Ka
 plan and Saharon Shelah\n
LOCATION:https://researchseminars.org/talk/OLS/189/
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