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Rado's conjecture Generalized Clubs club_AD Kurepa Hypothesis polarized partition relation Poset xbox Subtle tree property C-sequence Square-Brackets Partition Relations Interval topology on trees GMA Subnormal ideal weak square Club Guessing Microscopic Approach Local Club Condensation. specializable Souslin tree Well-behaved magma Antichain P-Ideal Dichotomy Non-saturation Postprocessing function Ineffable cardinal incompactness Almost countably chromatic square HOD Countryman line Amenable C-sequence 54G20 Coherent tree Hereditarily Lindelöf space Universal Sequences Greatly Mahlo SNR OCA Commutative projection system Weakly compact cardinal Shelah's Strong Hypothesis Almost Souslin Closed coloring L-space stationary reflection reflection principles Subtle cardinal Dushnik-Miller approachability ideal stick Generalized descriptive set theory Singular cardinals combinatorics Vanishing levels Strongly compact cardinal Successor of Regular Cardinal O-space Sierpinski's onto mapping principle Souslin Tree Respecting tree Slim tree Monotonically far Prikry-type forcing Cardinal function weak diamond Ascent Path square principles free Boolean algebra Knaster and friends Sigma-Prikry Singular cofinality Diamond-sharp Entangled linear order higher Baire space Prevalent singular cardinals S-Space stationary hitting Almost-disjoint family Hedetniemi's conjecture Chromatic number Filter reflection Lipschitz reduction Whitehead Problem indecomposable filter AIM forcing Open Access Knaster Uniformly coherent Parameterized proxy principle Precaliber Strong coloring PFA(S)[S] Distributive tree sap Forcing with side conditions Forcing Analytic sets super-Souslin tree Was Ulam right? Reduced Power countably metacompact Forcing Axioms Axiom R ZFC construction Subadditive Strongly Luzin set Hindman's Theorem Erdos Cardinal perfectly normal nonmeager set Rock n' Roll Erdos-Hajnal graphs strongly bounded groups transformations Jonsson cardinal PFA unbounded function full tree Ostaszewski square Dowker space Mandelbrot set Constructible Universe Cardinal Invariants Aronszajn tree weak Kurepa tree Luzin set Sakurai's Bell inequality Commutative cancellative semigroups positive partition relation regressive Souslin tree Foundations Minimal Walks Chang's conjecture Fast club Intersection model very good scale coloring number Fodor-type reflection Partition Relations Cohen real projective Boolean algebra Martin's Axiom Iterated forcing Absoluteness ccc Successor of Singular Cardinal Diamond Ascending path Rainbow sets Ramsey theory over partitions middle diamond Singular Density Large Cardinals Fat stationary set Nonspecial tree Reflecting stationary set Selective Ultrafilter free Souslin tree Diamond for trees Uniformization b-scale tensor product graph Small forcing diamond star Uniformly homogeneous Ulam matrix
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
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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
