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Absoluteness incompactness GMA specializable Souslin tree Knaster and friends Vanishing levels Rock n' Roll Entangled linear order SNR Hedetniemi's conjecture Respecting tree polarized partition relation PFA Slim tree Chang's conjecture ccc square principles Almost-disjoint family Martin's Axiom Precaliber Strongly compact cardinal Sakurai's Bell inequality Coherent tree Knaster HOD Rado's conjecture nonmeager set free Souslin tree reflection principles Well-behaved magma Ascent Path middle diamond Mandelbrot set Generalized Clubs Almost countably chromatic Analytic sets Distributive tree Large Cardinals Constructible Universe Microscopic Approach Antichain Ostaszewski square Diamond-sharp Hereditarily Lindelöf space Successor of Regular Cardinal Small forcing AIM forcing perfectly normal Cardinal Invariants tensor product graph coloring number Partition relations for trees Diamond for trees Open Access Souslin Tree Cardinal function Singular Density b-scale Closed coloring Whitehead Problem Countryman line Uniformly coherent stationary reflection Selective Ultrafilter strongly bounded groups Shelah's Strong Hypothesis Subtle tree property Fat stationary set Weakly compact cardinal Aronszajn tree Commutative projection system Reduced Power Interval topology on trees Erdos Cardinal Sierpinski's onto mapping principle Almost Souslin Monotonically far Axiom R C-sequence regressive Souslin tree positive partition relation Iterated forcing Ulam matrix approachability ideal Singular cardinals combinatorics Uniformly homogeneous Minimal Walks Generalized descriptive set theory Nonspecial tree Ineffable cardinal Diamond Was Ulam right? countably metacompact Ramsey theory over partitions O-space weak square Jonsson cardinal Ascending path Strong coloring Forcing Cohen real OCA Kurepa Hypothesis Commutative cancellative semigroups Universal Sequences Local Club Condensation. Poset super-Souslin tree Prevalent singular cardinals Successor of Singular Cardinal Amenable C-sequence Fodor-type reflection Rainbow sets projective Boolean algebra higher Baire space Parameterized proxy principle Uniformization Chromatic number Luzin set Non-saturation square stick 54G20 xbox Greatly Mahlo diamond star Postprocessing function L-space Forcing Axioms Reflecting stationary set very good scale weak diamond Singular cofinality transformations Partition Relations free Boolean algebra stationary hitting Erdos-Hajnal graphs weak Kurepa tree Subadditive ZFC construction P-Ideal Dichotomy Prikry-type forcing Forcing with side conditions Dowker space unbounded function Subtle cardinal club_AD indecomposable filter Lipschitz reduction PFA(S)[S] Hindman's Theorem sap Intersection model Foundations full tree Filter reflection Sigma-Prikry S-Space Square-Brackets Partition Relations Fast club Subnormal ideal Strongly Luzin set Dushnik-Miller Club Guessing
Category Archives: Publications
On the consistency strength of the Milner-Sauer conjecture
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 conjecture is consistent and known … Continue reading
Transforming rectangles into squares, with applications to strong colorings
Abstract: It is proved that every singular cardinal $\lambda$ admits a function $\textbf{rts}:[\lambda^+]^2\rightarrow[\lambda^+]^2$ that transforms rectangles into squares. That is, whenever $A,B$ are cofinal subsets of $\lambda^+$, we have $\textbf{rts}[A\circledast B]\supseteq C\circledast C$, for some cofinal subset $C\subseteq\lambda^+$. As a … Continue reading
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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