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Weakly compact cardinal Fat stationary set Partition Relations Distributive tree Local Club Condensation. Successor of Regular Cardinal O-space diamond star Ostaszewski square Hedetniemi's conjecture Club Guessing Cohen real Generalized Clubs Closed coloring Dushnik-Miller 54G20 projective Boolean algebra incompactness Aronszajn tree Antichain Almost countably chromatic middle diamond Absoluteness PFA Microscopic Approach transformations Poset Forcing weak Kurepa tree Knaster Ramsey theory over partitions Almost-disjoint family Was Ulam right regressive Souslin tree polarized partition relation Amenable C-sequence Generalized descriptive set theory stick Sakurai's Bell inequality Constructible Universe Almost Souslin Square-Brackets Partition Relations Fast club reflection principles PFA(S)[S] Luzin set Rado's conjecture free Souslin tree Singular Density Singular cardinals combinatorics b-scale weak diamond stationary hitting club_AD SNR Dowker space Slim tree OCA Vanishing levels Hindman's Theorem Axiom R nonmeager set higher Baire space Universal Sequences Chang's conjecture Selective Ultrafilter indecomposable ultrafilter Whitehead Problem strongly bounded groups Ineffable cardinal ZFC construction Sierpinski's onto mapping principle Coherent tree HOD Souslin Tree C-sequence Forcing Axioms Prikry-type forcing Filter reflection Strongly Luzin set Ulam matrix Martin's Axiom full tree free Boolean algebra Cardinal Invariants Iterated forcing Subadditive Erdos-Hajnal graphs Rock n' Roll Subtle cardinal Prevalent singular cardinals Erdos Cardinal Minimal Walks Nonspecial tree Uniformization Successor of Singular Cardinal Foundations Strong coloring square principles Diamond Shelah's Strong Hypothesis square Diamond-sharp GMA countably metacompact Precaliber Well-behaved magma stationary reflection Singular cofinality coloring number Subtle tree property Mandelbrot set Ascent Path Subnormal ideal P-Ideal Dichotomy S-Space Kurepa Hypothesis unbounded function specializable Souslin tree Knaster and friends Cardinal function Uniformly coherent Hereditarily Lindelöf space Sigma-Prikry Large Cardinals Non-saturation L-space Diamond for trees Analytic sets approachability ideal Fodor-type reflection Lipschitz reduction weak square positive partition relation tensor product graph ccc Reduced Power sap xbox Jonsson cardinal Uniformly homogeneous Rainbow sets Postprocessing function Commutative cancellative semigroups Small forcing Parameterized proxy principle Chromatic number very good scale Open Access super-Souslin tree Greatly Mahlo AIM forcing Reflecting stationary set
Category Archives: Publications
Sums of triples in Abelian groups
Joint work with Ido Feldman. Abstract. Motivated by a problem in additive Ramsey theory, we extend Todorcevic’s partitions of three-dimensional combinatorial cubes to handle additional three-dimensional objects. As a corollary, we get that if the continuum hypothesis fails, then for … Continue reading
A club guessing toolbox I
Joint work with Tanmay Inamdar. Abstract. Club guessing principles were introduced by Shelah as a weakening of Jensen’s diamond. Most spectacularly, they were used to prove Shelah’s ZFC bound on the power of the first singular cardinal. These principles have … Continue reading
Posted in Preprints, Squares and Diamonds
Tagged Club Guessing
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Ramsey theory over partitions II: Negative Ramsey relations and pump-up theorems
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, we concentrate on anti-Ramsey relations, or, as they are better known, strong colorings, and in … Continue reading
A new small Dowker space
Joint work with Roy Shalev and Stevo Todorcevic. Abstract. It is proved that if there exists a Luzin set, or if either the stick principle or $\diamondsuit(\mathfrak b)$ hold, then an instance of the guessing principle $\clubsuit_{AD}$ holds at the … Continue reading
Was Ulam right? II: Small width and general ideals
Joint work with Tanmay Inamdar. Abstract. We continue our study of Sierpinski-type colourings. In contrast to the prequel paper, we focus here on colourings for ideals stratified by their completeness degree. In particular, improving upon Ulam’s theorem and its extension … Continue reading
Posted in Partition Relations, Publications
Tagged 03E02, 03E35, 03E55, C-sequence, Open Access, Subnormal ideal, Ulam matrix, Was Ulam right
1 Comment
Complicated colorings, revisited
Joint work with Jing Zhang. Abstract. In a paper from 1997, Shelah asked whether $Pr_1(\lambda^+,\lambda^+,\lambda^+,\lambda)$ holds for every inaccessible cardinal $\lambda$. Here, we prove that an affirmative answer follows from $\square(\lambda^+)$. Furthermore, we establish that for every pair $\chi<\kappa$ of … Continue reading
Sigma-Prikry forcing III: Down to Aleph_omega
Joint work with Alejandro Poveda and Dima Sinapova. Abstract. We prove the consistency of the failure of the singular cardinals hypothesis at $\aleph_\omega$ together with the reflection of all stationary subsets of $\aleph_{\omega+1}$. This shows that two classical results of … Continue reading
Was Ulam right? I: Basic theory and subnormal ideals
Joint work with Tanmay Inamdar. Abstract. We introduce various coloring principles which generalize the so-called onto mapping principle of Sierpinski to larger cardinals and general ideals. We prove that these principles capture the notion of an Ulam matrix and allow … Continue reading
Knaster and friends III: Subadditive colorings
Joint work with Chris Lambie-Hanson. Abstract. We continue our study of strongly unbounded colorings, this time focusing on subadditive maps. In Part I of this series, we showed that, for many pairs of infinite cardinals $\theta < \kappa$, the existence … Continue reading
Posted in Partition Relations, Publications
Tagged Ascent Path, Knaster and friends, Open Access, P-Ideal Dichotomy, sap, square, Subadditive, Uniformly coherent
1 Comment
Strongest transformations
Joint work with Jing Zhang. Abstract. We continue our study of maps transforming high-dimensional complicated objects into squares of stationary sets. Previously, we proved that many such transformations exist in ZFC, and here we address the consistency of the strongest … Continue reading
Posted in Partition Relations, Publications
Tagged Diamond, Minimal Walks, square, Square-Brackets Partition Relations, stick, transformations, xbox
2 Comments
