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