Archives
Keywords
Fast club Intersection model Greatly Mahlo club_AD square principles Hindman's Theorem Singular cofinality Dushnik-Miller Analytic sets full tree Countryman line Foundations xbox Subadditive Uniformly coherent Ulam matrix AIM forcing Ascent Path Open Access projective Boolean algebra indecomposable ultrafilter Local Club Condensation. Generalized descriptive set theory Chang's conjecture ccc Singular Density Forcing Axioms Strongly Luzin set OCA ZFC construction Knaster stationary reflection Diamond for trees GMA Rock n' Roll strongly bounded groups Reflecting stationary set Filter reflection nonmeager set Subtle tree property Small forcing Constructible Universe Precaliber Respecting tree Ramsey theory over partitions Amenable C-sequence Sakurai's Bell inequality Axiom R Hereditarily Lindelöf space Cohen real Successor of Singular Cardinal L-space Subtle cardinal Whitehead Problem Rainbow sets Fat stationary set coloring number Prikry-type forcing free Boolean algebra Almost-disjoint family Almost countably chromatic countably metacompact Rado's conjecture Distributive tree reflection principles Generalized Clubs Well-behaved magma super-Souslin tree S-Space Successor of Regular Cardinal Knaster and friends approachability ideal Weakly compact cardinal Closed coloring Poset Slim tree Absoluteness Luzin set middle diamond Dowker space incompactness specializable Souslin tree HOD positive partition relation Erdos Cardinal PFA O-space stick Microscopic Approach Postprocessing function Antichain Nonspecial tree Uniformization weak square Was Ulam right? Strong coloring C-sequence Partition Relations Reduced Power Diamond-sharp Diamond stationary hitting Prevalent singular cardinals diamond star Commutative cancellative semigroups Aronszajn tree Vanishing levels square Club Guessing Iterated forcing Cardinal function Sigma-Prikry unbounded function Selective Ultrafilter Martin's Axiom b-scale Cardinal Invariants Minimal Walks Strongly compact cardinal weak Kurepa tree Almost Souslin Shelah's Strong Hypothesis PFA(S)[S] Ostaszewski square Uniformly homogeneous 54G20 Sierpinski's onto mapping principle Commutative projection system Kurepa Hypothesis Mandelbrot set Non-saturation Forcing very good scale tensor product graph Ineffable cardinal Parameterized proxy principle transformations Singular cardinals combinatorics P-Ideal Dichotomy Large Cardinals Jonsson cardinal polarized partition relation weak diamond Square-Brackets Partition Relations Lipschitz reduction Universal Sequences Chromatic number Hedetniemi's conjecture Fodor-type reflection higher Baire space Erdos-Hajnal graphs SNR free Souslin tree sap regressive Souslin tree Subnormal ideal Coherent tree Souslin Tree
Category Archives: Blog
A strong form of König’s lemma
A student proposed to me the following strong form of König’s lemma: Conjecture. Suppose that
Posted in Blog
2 Comments
Prikry forcing may add a Souslin tree
A celebrated theorem of Shelah states that adding a Cohen real introduces a Souslin tree. Are there any other examples of notions of forcing that add a
The reflection principle
A few years ago, in this paper, I introduced the following reflection principle: Definition.
Posted in Blog
Tagged reflection principles, square, stationary reflection, Weakly compact cardinal
Leave a comment
Prolific Souslin trees
In a paper from 1971, Erdos and Hajnal asked whether (assuming CH) every coloring witnessing
Posted in Blog, Expository
Tagged Rainbow sets, Souslin Tree, Square-Brackets Partition Relations
Leave a comment
Generalizations of Martin’s Axiom and the well-met condition
Recall that Martin’s Axiom asserts that for every partial order
Many diamonds from just one
Recall Jensen’s diamond principle over a stationary subset
Square principles
Since the birth of Jensen’s original Square principle, many variations of the principle were introduced and intensively studied. Asaf Karagila suggested me today to put some order into all of these principles. Here is a trial. Definition. A square principle … Continue reading
Partitioning the club guessing
In a recent paper, I am making use of the following fact. Theorem (Shelah, 1997). Suppose that
Walk on countable ordinals: the characteristics
In this post, we shall present a few aspects of the method of walk on ordinals (focusing on countable ordinals), record its characteristics, and verify some of their properties. All definitions and results in this post are due to Todorcevic. … Continue reading
