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Local Club Condensation. Erdos Cardinal tensor product graph Souslin Tree projective Boolean algebra free Souslin tree AIM forcing Club Guessing Diamond Slim tree PFA Sakurai's Bell inequality Respecting tree Lipschitz reduction Filter reflection full tree ccc Diamond-sharp Antichain sap square principles Partition Relations Strong coloring Sierpinski's onto mapping principle Foundations Coherent tree countably metacompact GMA Almost countably chromatic free Boolean algebra higher Baire space Strongly compact cardinal Diamond for trees weak Kurepa tree Hedetniemi's conjecture nonmeager set Vanishing levels Rainbow sets Subnormal ideal Poset coloring number Hereditarily Lindelöf space Prikry-type forcing S-Space Erdos-Hajnal graphs Generalized Clubs Square-Brackets Partition Relations square SNR transformations Successor of Regular Cardinal Was Ulam right diamond star weak diamond Singular cofinality indecomposable ultrafilter Kurepa Hypothesis Generalized descriptive set theory b-scale Forcing Axioms Fat stationary set Knaster and friends Cardinal Invariants Whitehead Problem Almost-disjoint family Knaster PFA(S)[S] Small forcing Large Cardinals Reflecting stationary set Non-saturation Closed coloring Well-behaved magma weak square Commutative projection system Subtle cardinal Cohen real 54G20 unbounded function Nonspecial tree Sigma-Prikry Iterated forcing OCA Ostaszewski square Chromatic number very good scale Analytic sets reflection principles polarized partition relation ZFC construction Fodor-type reflection Fast club P-Ideal Dichotomy incompactness Amenable C-sequence HOD Greatly Mahlo Universal Sequences C-sequence Mandelbrot set xbox stick specializable Souslin tree Absoluteness Ramsey theory over partitions Ascent Path middle diamond Luzin set Strongly Luzin set stationary reflection Postprocessing function Martin's Axiom Weakly compact cardinal Subtle tree property Parameterized proxy principle L-space Dowker space Hindman's Theorem Ineffable cardinal Singular cardinals combinatorics Uniformly coherent Countryman line Shelah's Strong Hypothesis Precaliber strongly bounded groups Singular Density Selective Ultrafilter Prevalent singular cardinals Dushnik-Miller Jonsson cardinal Subadditive regressive Souslin tree Uniformization super-Souslin tree Open Access Distributive tree Minimal Walks Aronszajn tree Cardinal function Rock n' Roll Successor of Singular Cardinal Chang's conjecture Axiom R Commutative cancellative semigroups approachability ideal Intersection model Forcing Ulam matrix Uniformly homogeneous stationary hitting O-space club_AD Almost Souslin Reduced Power positive partition relation Microscopic Approach Rado's conjecture Constructible Universe
Category Archives: Publications
A counterexample related to a theorem of Komjáth and Weiss
Joint work with Rodrigo Rey Carvalho. Abstract. In a paper from 1987, Komjath and Weiss proved that for every regular topological space $X$ of character less than $\mathfrak b$, if $X\rightarrow(\text{top }{\omega+1})^1_\omega$, then $X\rightarrow(\text{top }{\alpha})^1_\omega$ for all $\alpha<\omega_1$. In addition, … Continue reading
Posted in Partition Relations, Preprints, Topology
Tagged 03E02, 54G20, Prikry-type forcing, ZFC construction
Comments Off on A counterexample related to a theorem of Komjáth and Weiss
A Shelah group in ZFC
Joint work with Márk Poór. Abstract. In a paper from 1980, Shelah constructed an uncountable group all of whose proper subgroups are countable. Assuming the continuum hypothesis, he constructed an uncountable group $G$ that moreover admits an integer $n$ satisfying … Continue reading
Posted in Groups, Preprints
Tagged 03E02, 03E75, 20A15, 20E15, 20F06, Jonsson cardinal, Strong coloring, strongly bounded groups, Subadditive, ZFC construction
2 Comments
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
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
