Archives
Keywords
Coherent tree Slim tree OCA Subadditive Ostaszewski square Knaster and friends Postprocessing function transformations Intersection model square Entangled linear order Jonsson cardinal Non-saturation incompactness Interval topology on trees Countryman line Partition Relations Rainbow sets Absoluteness Strong coloring Foundations Forcing Axioms Hereditarily Lindelöf space higher Baire space HOD Reflecting stationary set Was Ulam right? perfectly normal Iterated forcing Closed coloring countably metacompact Aronszajn tree GMA Cardinal function full tree 54G20 Constructible Universe Fat stationary set Diamond-sharp Antichain Parameterized proxy principle Dowker space Successor of Regular Cardinal Rado's conjecture Uniformly coherent nonmeager set Prevalent singular cardinals Forcing Singular cardinals combinatorics Strongly Luzin set indecomposable filter Local Club Condensation. Erdos-Hajnal graphs Monotonically far unbounded function Filter reflection super-Souslin tree stick Diamond for trees ccc Chang's conjecture Distributive tree Almost countably chromatic Luzin set Fodor-type reflection O-space Analytic sets Hedetniemi's conjecture Large Cardinals Kurepa Hypothesis Dushnik-Miller Lipschitz reduction reflection principles tensor product graph Weakly compact cardinal PFA(S)[S] Generalized Clubs Singular cofinality Nonspecial tree Erdos Cardinal Strongly compact cardinal SNR Subtle tree property Sigma-Prikry positive partition relation Greatly Mahlo Ascent Path Well-behaved magma Sakurai's Bell inequality Mandelbrot set Prikry-type forcing diamond star Diamond Microscopic Approach Subtle cardinal Amenable C-sequence Universal Sequences Respecting tree P-Ideal Dichotomy Singular Density xbox C-sequence weak diamond Uniformly homogeneous free Souslin tree stationary hitting Club Guessing weak Kurepa tree Successor of Singular Cardinal b-scale coloring number Shelah's Strong Hypothesis Precaliber sap Uniformization Open Access square principles Knaster specializable Souslin tree Sierpinski's onto mapping principle PFA Ramsey theory over partitions very good scale Commutative cancellative semigroups Ineffable cardinal Rock n' Roll approachability ideal Commutative projection system Cohen real stationary reflection strongly bounded groups Selective Ultrafilter Almost Souslin Fast club Souslin Tree Chromatic number Whitehead Problem Martin's Axiom projective Boolean algebra Vanishing levels Forcing with side conditions weak square Small forcing free Boolean algebra L-space ZFC construction Generalized descriptive set theory Minimal Walks Subnormal ideal Reduced Power regressive Souslin tree Hindman's Theorem middle diamond Square-Brackets Partition Relations polarized partition relation Poset Axiom R Ascending path Cardinal Invariants AIM forcing Ulam matrix Partition relations for trees club_AD Almost-disjoint family S-Space
Tag Archives: indecomposable filter
2025 Annual conference of the IMU
I gave an invited talk at the Set Theory session of the annual meeting of the IMU, July 2025. Talk Title: What my co-authors taught me about indecomposability Abstract: Ulam’s measure problem studies when there is a countably-additive two-valued measure … Continue reading
Posted in Invited Talks
Tagged indecomposable filter
Comments Off on 2025 Annual conference of the IMU
Was Ulam right? III: Indecomposable ideals
Joint work with Tanmay Inamdar. Abstract. We continue our study of Ulam’s measure problem. In contrast to our previous works, we shift our focus from measures stratified by their additivity, to measures stratified by their indecomposability. The breakthrough here is … Continue reading
Ketonen’s question and other cardinal sins
Joint work with Zhixing You and Jiachen Yuan. Abstract. Answering a question of Ketonen from the late 1970’s, it is proved that a weakly compact cardinal carrying an indecomposable ultrafilter need not be measurable. The result is obtained by analyzing … Continue reading
Squares, ultrafilters and forcing axioms
Joint work with Chris Lambie-Hanson and Jing Zhang. Abstract. We study the interplay of the three families of combinatorial objects or principles. Specifically, we show the following. Strong forcing axioms, in general incompatible with the existence of indexed squares, can … 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
