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Kurepa Hypothesis positive partition relation very good scale Parameterized proxy principle Intersection model L-space unbounded function higher Baire space Successor of Regular Cardinal Chromatic number Rado's conjecture Knaster PFA(S)[S] Generalized descriptive set theory Uniformly coherent Almost countably chromatic Lipschitz reduction Respecting tree Minimal Walks Cohen real Reflecting stationary set ZFC construction GMA Erdos Cardinal Foundations square Partition Relations C-sequence Ramsey theory over partitions Singular Density Singular cofinality 54G20 Reduced Power projective Boolean algebra diamond star free Boolean algebra weak diamond Iterated forcing SNR HOD Ascent Path Universal Sequences Square-Brackets Partition Relations Distributive tree Microscopic Approach Non-saturation Subtle cardinal Forcing Uniformization transformations Jonsson cardinal P-Ideal Dichotomy Small forcing Strongly compact cardinal O-space Almost-disjoint family approachability ideal stick Strong coloring regressive Souslin tree S-Space Sigma-Prikry free Souslin tree coloring number Cardinal Invariants Antichain Subtle tree property Shelah's Strong Hypothesis Constructible Universe Open Access Club Guessing Commutative cancellative semigroups tensor product graph Souslin Tree Was Ulam right? Chang's conjecture OCA Commutative projection system Precaliber Forcing Axioms Diamond for trees countably metacompact Hedetniemi's conjecture Diamond-sharp Knaster and friends stationary hitting Countryman line Ostaszewski square indecomposable filter Amenable C-sequence middle diamond Singular cardinals combinatorics Subnormal ideal ccc Dushnik-Miller Closed coloring Slim tree strongly bounded groups weak square Rainbow sets Prikry-type forcing Strongly Luzin set super-Souslin tree Absoluteness Diamond Successor of Singular Cardinal Greatly Mahlo square principles Postprocessing function Analytic sets Axiom R Erdos-Hajnal graphs Selective Ultrafilter Whitehead Problem Local Club Condensation. nonmeager set AIM forcing Poset Luzin set Fat stationary set Fast club Dowker space Filter reflection Sakurai's Bell inequality Large Cardinals Weakly compact cardinal weak Kurepa tree Martin's Axiom Mandelbrot set Hindman's Theorem club_AD Well-behaved magma Generalized Clubs incompactness specializable Souslin tree Uniformly homogeneous b-scale Coherent tree xbox Rock n' Roll Nonspecial tree Aronszajn tree Almost Souslin Ineffable cardinal Vanishing levels stationary reflection reflection principles polarized partition relation full tree Hereditarily Lindelöf space Cardinal function Ulam matrix Prevalent singular cardinals PFA Fodor-type reflection Sierpinski's onto mapping principle sap Subadditive
Category Archives: Blog
An inconsistent form of club guessing
In this post, we shall present an answer (due to P. Larson) to a question by A. Primavesi concerning a certain strong form of club guessing. We commence with recalling Shelah’s concept of club guessing. Concept (Shelah). Given a regular … Continue reading
c.c.c. forcing without combinatorics
In this post, we shall discuss a short paper by Alan Mekler from 1984, concerning a non-combinatorial verification of the c.c.c. property for forcing notions. Recall that a notion of forcing
Dushnik-Miller for singular cardinals (part 2)
In the first post on this subject, we provided a proof of
Posted in Blog, Expository
Tagged Dushnik-Miller, Partition Relations, Singular cardinals combinatorics
27 Comments
Dushnik-Miller for regular cardinals (part 2)
In this post, we shall provide a proof of Todorcevic’s theorem, that
Posted in Blog, Expository
Tagged b-scale, Dushnik-Miller, Partition Relations, Square-Brackets Partition Relations
5 Comments
Dushnik-Miller for singular cardinals (part 1)
Continuing the previous post, let us now prove the following. Theorem (Erdos-Dushnik-Miller, 1941). For every singular cardinal λ, we have:
Dushnik-Miller for regular cardinals (part 1)
This is the first out of a series of posts on the following theorem. Theorem (Erdos-Dushnik-Miller, 1941). For every infinite cardinal
The order-type of clubs in a square sequence
Recall Jensen’s notion of square: Definition (Jensen): For an infinite cardinal
Music Video: “Wide Open” by Jenny Mayhem
Did you notice the toolbar at the bottom of my posts? e.g.:
Posted in Blog, OffMath
2 Comments
