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xbox Cohen real Strong coloring Amenable C-sequence Subtle cardinal free Boolean algebra Analytic sets Strongly compact cardinal Fast club Aronszajn tree Diamond-sharp b-scale positive partition relation Ostaszewski square Uniformly homogeneous Hedetniemi's conjecture S-Space Dowker space Singular cardinals combinatorics transformations Cardinal function Singular cofinality Non-saturation Strongly Luzin set Reflecting stationary set Subadditive Sigma-Prikry club_AD tensor product graph weak square diamond star OCA Iterated forcing GMA square principles ZFC construction SNR Almost-disjoint family Universal Sequences polarized partition relation Chromatic number higher Baire space Poset countably metacompact very good scale Rado's conjecture Large Cardinals Subtle tree property stick Forcing Kurepa Hypothesis Fodor-type reflection square Parameterized proxy principle Coherent tree Luzin set Prikry-type forcing Knaster Absoluteness perfectly normal Monotonically far free Souslin tree Greatly Mahlo Jonsson cardinal weak Kurepa tree Entangled linear order Microscopic Approach unbounded function Rock n' Roll Slim tree HOD Interval topology on trees Martin's Axiom middle diamond Hereditarily Lindelöf space O-space Uniformization Selective Ultrafilter Partition Relations AIM forcing indecomposable filter Club Guessing C-sequence Closed coloring Vanishing levels Uniformly coherent Ramsey theory over partitions Distributive tree Diamond for trees Open Access full tree Ascent Path PFA strongly bounded groups Fat stationary set Foundations Axiom R Mandelbrot set coloring number sap Reduced Power super-Souslin tree Souslin Tree Respecting tree regressive Souslin tree Antichain reflection principles Filter reflection P-Ideal Dichotomy Nonspecial tree weak diamond Well-behaved magma PFA(S)[S] Successor of Regular Cardinal Minimal Walks ccc Subnormal ideal Successor of Singular Cardinal Weakly compact cardinal stationary reflection specializable Souslin tree approachability ideal Ulam matrix Was Ulam right? Hindman's Theorem Constructible Universe Almost Souslin Shelah's Strong Hypothesis incompactness Almost countably chromatic Sakurai's Bell inequality projective Boolean algebra Generalized descriptive set theory Knaster and friends Commutative cancellative semigroups Local Club Condensation. Lipschitz reduction Ineffable cardinal 54G20 Rainbow sets Whitehead Problem Intersection model L-space Cardinal Invariants Small forcing Erdos-Hajnal graphs Square-Brackets Partition Relations Prevalent singular cardinals Generalized Clubs Precaliber Chang's conjecture Forcing Axioms Singular Density Countryman line Sierpinski's onto mapping principle Forcing with side conditions Diamond nonmeager set stationary hitting Erdos Cardinal Partition relations for trees Ascending path Postprocessing function Commutative projection system Dushnik-Miller
Tag Archives: Martin’s Axiom
Ramsey theory over partitions I: Positive Ramsey relations from forcing axioms
Joint work with Menachem Kojman and Juris Steprāns. Abstract. In this series of papers, we advance Ramsey theory of colorings over partitions. In this part, a correspondence between anti-Ramsey properties of partitions and chain conditions of the natural forcing notions … Continue reading
Posted in Partition Relations, Publications
Tagged 03E02, 03E17, 03E35, GMA, Martin's Axiom, positive partition relation, Ramsey theory over partitions
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Generalizations of Martin’s Axiom and the well-met condition
Recall that Martin’s Axiom asserts that for every partial order $\mathbb P$ satisfying c.c.c., and for any family $\mathcal D$ of $<2^{\aleph_0}$ many dense subsets of $\mathbb P$, there exists a directed subset $G$ of $\mathbb P$ such that $G\cap … Continue reading
Posted in Blog, Expository
Tagged ccc, Forcing Axioms, GMA, Martin's Axiom, Uniformization
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Shelah’s solution to Whitehead’s problem
Whitehead problem notes in hebrew : Table of contents Chapter 0 Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 References
