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C-sequence Analytic sets weak Kurepa tree Reduced Power Slim tree PFA(S)[S] middle diamond club_AD Club Guessing stationary hitting O-space Forcing Almost Souslin Was Ulam right? diamond star Cardinal Invariants free Boolean algebra Ascent Path Commutative cancellative semigroups Precaliber Chang's conjecture Iterated forcing very good scale indecomposable ultrafilter Countryman line stick Nonspecial tree Selective Ultrafilter GMA Forcing Axioms Fat stationary set Distributive tree Knaster and friends Erdos-Hajnal graphs Partition Relations Knaster incompactness Ulam matrix Local Club Condensation. Sierpinski's onto mapping principle 54G20 Cohen real PFA OCA Hereditarily Lindelöf space AIM forcing Martin's Axiom super-Souslin tree coloring number nonmeager set Coherent tree b-scale unbounded function Filter reflection Intersection model S-Space Diamond Axiom R Aronszajn tree Parameterized proxy principle Sigma-Prikry Open Access Diamond for trees higher Baire space Strongly compact cardinal Uniformly homogeneous Large Cardinals Chromatic number Singular cofinality L-space stationary reflection Lipschitz reduction Rado's conjecture xbox Almost-disjoint family Rainbow sets Subadditive Dushnik-Miller Subtle tree property Prevalent singular cardinals ccc Uniformization square Dowker space Ostaszewski square regressive Souslin tree Vanishing levels Sakurai's Bell inequality Almost countably chromatic Non-saturation polarized partition relation Singular Density Commutative projection system Reflecting stationary set tensor product graph ZFC construction Diamond-sharp Uniformly coherent Amenable C-sequence Fodor-type reflection countably metacompact Successor of Regular Cardinal positive partition relation Greatly Mahlo Successor of Singular Cardinal Minimal Walks Antichain P-Ideal Dichotomy Shelah's Strong Hypothesis Jonsson cardinal Closed coloring Souslin Tree Absoluteness Hindman's Theorem sap projective Boolean algebra Universal Sequences Mandelbrot set Prikry-type forcing square principles free Souslin tree Fast club Whitehead Problem Subnormal ideal Kurepa Hypothesis Weakly compact cardinal Ramsey theory over partitions weak square full tree approachability ideal Square-Brackets Partition Relations HOD Luzin set specializable Souslin tree Hedetniemi's conjecture weak diamond Strongly Luzin set Small forcing Rock n' Roll reflection principles Poset Singular cardinals combinatorics Microscopic Approach Subtle cardinal Foundations Generalized descriptive set theory SNR strongly bounded groups Strong coloring Well-behaved magma transformations Constructible Universe Erdos Cardinal Generalized Clubs Cardinal function Postprocessing function Respecting tree Ineffable cardinal
Tag Archives: Minimal Walks
Walks on uncountable ordinals and non-structure theorems for higher Aronszajn lines
Joint work with Tanmay Inamdar. Abstract. We investigate global structural properties of linear orders of a fixed infinite size. It is classical that the countable linear orders and the continuum-sized orders exhibit contrasting behaviours. Modern results show that strong extensions … Continue reading
Complicated colorings, revisited
Joint work with Jing Zhang. Abstract. In a paper from 1997, Shelah asked whether
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
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Transformations of the transfinite plane
Joint work with Jing Zhang. Abstract. We study the existence of transformations of the transfinite plane that allow one to reduce Ramsey-theoretic statements concerning uncountable Abelian groups into classical partition relations for uncountable cardinals. To exemplify: we prove that for every … Continue reading
11th Young Set Theory Workshop, June 2018
I gave a 4-lecture tutorial at the 11th Young Set Theory Workshop, Lausanne, June 2018. Title: In praise of C-sequences. Abstract. Ulam and Solovay showed that any stationary set may be split into two. Is it also the case that … Continue reading
Posted in Invited Talks
Tagged Aronszajn tree, C-sequence, incompactness, Knaster, Minimal Walks, Postprocessing function, square
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6th European Set Theory Conference, July 2017
I gave a 3-lecture tutorial at the 6th European Set Theory Conference in Budapest, July 2017. Title: Strong colorings and their applications. Abstract. Consider the following questions. Is the product of two
Posted in Invited Talks, Open Problems
Tagged b-scale, Cohen real, Luzin set, Minimal Walks, Souslin Tree, Square-Brackets Partition Relations
4 Comments
Distributive Aronszajn trees
Joint work with Ari Meir Brodsky. Abstract. Ben-David and Shelah proved that if
Square with built-in diamond-plus
Joint work with Ralf Schindler. Abstract. We formulate combinatorial principles that combine the square principle with various strong forms of diamond, and prove that the strongest amongst them holds in
Posted in Publications, Squares and Diamonds
Tagged 03E05, 03E45, Almost Souslin, diamond star, Kurepa Hypothesis, Minimal Walks, Respecting tree, square, xbox
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Chain conditions of products, and weakly compact cardinals
Abstract. The history of productivity of the
Posted in Partition Relations, Publications
Tagged Aronszajn tree, ccc, Fat stationary set, Minimal Walks, square, Weakly compact cardinal
2 Comments
Complicated colorings
Abstract. If
Posted in Partition Relations, Publications
Tagged Minimal Walks, Open Access, Square-Brackets Partition Relations
2 Comments
