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