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super-Souslin tree Whitehead Problem weak diamond unbounded function sap projective Boolean algebra Forcing Axioms SNR Uniformly coherent Martin's Axiom Lipschitz reduction Small forcing Erdos Cardinal stick Rado's conjecture Forcing with side conditions Jonsson cardinal O-space Poset Square-Brackets Partition Relations AIM forcing Ulam matrix Aronszajn tree Antichain square Respecting tree countably metacompact Prevalent singular cardinals Ramsey theory over partitions Ascending path Strongly compact cardinal Closed coloring Partition relations for trees Open Access diamond star free Boolean algebra Commutative projection system Dowker space middle diamond Large Cardinals Sakurai's Bell inequality stationary hitting ccc reflection principles Hedetniemi's conjecture Ineffable cardinal Non-saturation Subtle cardinal Hindman's Theorem Mandelbrot set higher Baire space Luzin set PFA(S)[S] P-Ideal Dichotomy Strong coloring specializable Souslin tree Chromatic number Interval topology on trees Forcing Strongly Luzin set Minimal Walks weak Kurepa tree Countryman line Parameterized proxy principle Vanishing levels Singular cardinals combinatorics Sierpinski's onto mapping principle Subnormal ideal 54G20 Ascent Path HOD transformations Fat stationary set positive partition relation Ostaszewski square Erdos-Hajnal graphs Weakly compact cardinal Reduced Power b-scale club_AD square principles Kurepa Hypothesis xbox Local Club Condensation. Diamond for trees Almost-disjoint family free Souslin tree Cohen real indecomposable filter Diamond-sharp Constructible Universe Diamond Subtle tree property approachability ideal Generalized descriptive set theory Commutative cancellative semigroups Foundations Precaliber Successor of Regular Cardinal Amenable C-sequence Entangled linear order Absoluteness Greatly Mahlo Almost Souslin incompactness very good scale Sigma-Prikry Cardinal Invariants Selective Ultrafilter regressive Souslin tree strongly bounded groups Almost countably chromatic Chang's conjecture perfectly normal coloring number Iterated forcing PFA Shelah's Strong Hypothesis Baumgartner's square Postprocessing function S-Space Universal Sequences Generalized Clubs Distributive tree Dushnik-Miller Fodor-type reflection Partition Relations Singular Density Souslin Tree nonmeager set Filter reflection Reflecting stationary set polarized partition relation Uniformization C-sequence OCA stationary reflection Well-behaved magma full tree Cardinal function Knaster and friends Monotonically far Fast club Nonspecial tree Intersection model Prikry-type forcing GMA Microscopic Approach tensor product graph Was Ulam right? L-space Uniformly homogeneous Analytic sets weak square Slim tree Coherent tree Axiom R Hereditarily Lindelöf space Singular cofinality ZFC construction Rainbow sets Club Guessing Successor of Singular Cardinal Rock n' Roll Subadditive Knaster
Tag Archives: Lipschitz reduction
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
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Tagged Lipschitz reduction, Partition relations for trees
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Fake Reflection
Joint work with Gabriel Fernandes and Miguel Moreno. Abstract. We introduce a generalization of stationary set reflection which we call filter reflection, and show it is compatible with the axiom of constructibility as well as with strong forcing axioms. We … Continue reading
Inclusion modulo nonstationary
Joint work with Gabriel Fernandes and Miguel Moreno. Abstract. A classical theorem of Hechler asserts that the structure $\left(\omega^\omega,\le^*\right)$ is universal in the sense that for any $\sigma$-directed poset $\mathbb P$ with no maximal element, there is a ccc forcing … Continue reading
