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Ulam matrix PFA weak diamond Square-Brackets Partition Relations Local Club Condensation. Amenable C-sequence Almost Souslin Subadditive coloring number Interval topology on trees Cardinal function regressive Souslin tree Precaliber Chang's conjecture Dowker space Prikry-type forcing Erdos Cardinal Strongly compact cardinal Vanishing levels Lipschitz reduction Commutative cancellative semigroups GMA positive partition relation Hereditarily Lindelöf space club_AD Uniformly coherent Cardinal Invariants tensor product graph specializable Souslin tree Uniformization free Souslin tree Postprocessing function Constructible Universe nonmeager set indecomposable filter Hindman's Theorem Strong coloring Parameterized proxy principle Subtle tree property full tree Jonsson cardinal SNR approachability ideal Well-behaved magma Singular cofinality reflection principles Rainbow sets Ineffable cardinal Mandelbrot set Coherent tree Generalized Clubs incompactness higher Baire space Small forcing Antichain Generalized descriptive set theory Axiom R polarized partition relation Sigma-Prikry Non-saturation Ostaszewski square Poset Subnormal ideal xbox weak square Diamond Ascent Path Analytic sets Reduced Power Shelah's Strong Hypothesis Whitehead Problem square countably metacompact Respecting tree Large Cardinals HOD Successor of Singular Cardinal transformations Chromatic number Selective Ultrafilter very good scale Microscopic Approach sap unbounded function Countryman line Kurepa Hypothesis AIM forcing Diamond-sharp Erdos-Hajnal graphs Knaster Sierpinski's onto mapping principle Nonspecial tree ZFC construction Universal Sequences Intersection model Fat stationary set Foundations Distributive tree middle diamond Singular Density Fodor-type reflection b-scale Minimal Walks Sakurai's Bell inequality Fast club Knaster and friends Entangled linear order Almost-disjoint family strongly bounded groups super-Souslin tree square principles Rado's conjecture 54G20 Absoluteness Strongly Luzin set Uniformly homogeneous Weakly compact cardinal Partition relations for trees PFA(S)[S] stationary hitting ccc projective Boolean algebra Diamond for trees Prevalent singular cardinals Forcing Cohen real Subtle cardinal Forcing with side conditions free Boolean algebra Greatly Mahlo Hedetniemi's conjecture Almost countably chromatic Filter reflection Souslin Tree Commutative projection system Rock n' Roll Iterated forcing L-space diamond star O-space Ramsey theory over partitions Dushnik-Miller S-Space OCA Slim tree Open Access Forcing Axioms P-Ideal Dichotomy Singular cardinals combinatorics Reflecting stationary set Ascending path Partition Relations Club Guessing C-sequence Was Ulam right? Monotonically far Luzin set stationary reflection Closed coloring Martin's Axiom weak Kurepa tree Successor of Regular Cardinal stick perfectly normal Aronszajn tree
Author Archives: Assaf Rinot
Antichains in partially ordered sets of singular cofinality
Abstract: In their paper from 1981, Milner and Sauer conjectured that for any poset $\mathbb P$, if $\text{cf}(\mathbb P)$ is a singular cardinal $\lambda$, then $\mathbb P$ must contain an antichain of size $\text{cf}(\lambda)$. The main result of of this … Continue reading
Posted in Publications, Singular Cardinals Combinatorics
Tagged 03E04, 03E35, 06A07, Antichain, Poset, Singular cofinality
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The Ostaszewski square, and homogeneous Souslin trees
Abstract: Assume GCH and let $\lambda$ denote an uncountable cardinal. We prove that if $\square_\lambda$ holds, then this may be witnessed by a coherent sequence $\left\langle C_\alpha \mid \alpha<\lambda^+\right\rangle$ with the following remarkable guessing property: For every sequence $\langle A_i\mid i<\lambda\rangle$ … Continue reading
Posted in Publications, Souslin Hypothesis, Squares and Diamonds
Tagged 03E05, 03E35, Club Guessing, Fat stationary set, Ostaszewski square, Souslin Tree
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Infinite Combinatorial Topology
Back in 2005, as a master student, I attended a course by Boaz Tsaban, entitled “Infinite Combinatorial Topology”. A friend and I decided to produce lecture notes, but in a somewhat loose sense, that is: we sometimes omit material given … Continue reading
Posted in Notes
Tagged b-scale, Cardinal function, Cardinal Invariants, Hereditarily Lindelöf space
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