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Tag Archives: Partition relations for trees
Partition relations for trees I: Incomparable trees
Joint work with Tanmay Inamdar. Abstract. Todorcevic proved that Martin’s axiom implies that every two coherent $\aleph_1$-Aronszajn trees are comparable. Here, from cardinal arithmetic assumptions, we obtain the failure of the analogous statement for higher trees. In particular, for every … Continue reading
Posted in Partition Relations, Preprints
Tagged Lipschitz reduction, Partition relations for trees
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Walks on uncountable ordinals and non-structure theorems for higher Aronszajn lines
Joint work with Tanmay Inamdar. Abstract. We investigate global structural properties of linear orders of a fixed infinite size. It is classical that the countable linear orders and the continuum-sized orders exhibit contrasting behaviours. Modern results show that strong extensions … Continue reading
Posted in Basis problems, Partition Relations, Preprints
Tagged Aronszajn tree, Ascending path, Club Guessing, Countryman line, Entangled linear order, Minimal Walks, Monotonically far, Partition relations for trees, Strong coloring, Subtle tree property, Vanishing levels, ZFC construction
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