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Rainbow sets Slim tree Prikry-type forcing ZFC construction Constructible Universe Uniformly homogeneous Filter reflection Knaster Subtle cardinal PFA(S)[S] Partition Relations Luzin set Cardinal Invariants square Successor of Singular Cardinal Ulam matrix 54G20 Vanishing levels Uniformly coherent Singular cofinality weak diamond Diamond for trees Distributive tree full tree Shelah's Strong Hypothesis tensor product graph positive partition relation Chromatic number Strongly Luzin set Dushnik-Miller specializable Souslin tree strongly bounded groups approachability ideal higher Baire space Selective Ultrafilter stationary reflection Sakurai's Bell inequality SNR Sigma-Prikry Jonsson cardinal Antichain Club Guessing Mandelbrot set Almost countably chromatic Commutative cancellative semigroups Ascent Path Square-Brackets Partition Relations Foundations Souslin Tree incompactness GMA stationary hitting Chang's conjecture Erdos Cardinal Analytic sets perfectly normal Precaliber Strong coloring Weakly compact cardinal Diamond-sharp Fast club Universal Sequences polarized partition relation PFA Successor of Regular Cardinal Non-saturation C-sequence Diamond Martin's Axiom unbounded function Ramsey theory over partitions free Souslin tree Fat stationary set Kurepa Hypothesis Sierpinski's onto mapping principle Aronszajn tree O-space HOD Coherent tree Absoluteness Commutative projection system Intersection model Open Access Local Club Condensation. Lipschitz reduction Closed coloring very good scale transformations Subnormal ideal Fodor-type reflection Reflecting stationary set Small forcing Axiom R reflection principles Microscopic Approach Almost Souslin Rado's conjecture Monotonically far countably metacompact sap Interval topology on trees Singular Density stick Nonspecial tree square principles Iterated forcing Poset projective Boolean algebra AIM forcing Rock n' Roll weak square b-scale Respecting tree Erdos-Hajnal graphs Knaster and friends Postprocessing function Well-behaved magma Hindman's Theorem Cardinal function Uniformization Generalized descriptive set theory Cohen real Whitehead Problem Minimal Walks nonmeager set super-Souslin tree OCA weak Kurepa tree indecomposable filter Strongly compact cardinal Greatly Mahlo Entangled linear order Generalized Clubs coloring number Large Cardinals Parameterized proxy principle Prevalent singular cardinals xbox Was Ulam right? Dowker space Partition relations for trees club_AD L-space S-Space middle diamond Ostaszewski square Forcing with side conditions ccc Forcing Axioms Subadditive Almost-disjoint family Ineffable cardinal Hereditarily Lindelöf space regressive Souslin tree Forcing Reduced Power Singular cardinals combinatorics Ascending path Hedetniemi's conjecture Amenable C-sequence Countryman line diamond star Subtle tree property P-Ideal Dichotomy free Boolean algebra
Category Archives: Publications
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
Fake Reflection
Joint work with Gabriel Fernandes and Miguel Moreno. Abstract. We introduce a generalization of stationary set reflection which we call filter reflection, and show it is compatible with the axiom of constructibility as well as with strong forcing axioms. We … Continue reading
A microscopic approach to Souslin-tree constructions. Part II
Joint work with Ari Meir Brodsky. Abstract. In Part I of this series, we presented the microscopic approach to Souslin-tree constructions, and argued that all known $\diamondsuit$-based constructions of Souslin trees with various additional properties may be rendered as applications of … Continue reading
Sigma-Prikry forcing II: Iteration Scheme
Joint work with Alejandro Poveda and Dima Sinapova. Abstract. In Part I of this series, we introduced a class of notions of forcing which we call $\Sigma$-Prikry, and showed that many of the known Prikry-type notions of forcing that centers … Continue reading
Knaster and friends II: The C-sequence number
Joint work with Chris Lambie-Hanson. Abstract. Motivated by a characterization of weakly compact cardinals due to Todorcevic, we introduce a new cardinal characteristic, the C-sequence number, which can be seen as a measure of the compactness of a regular uncountable … Continue reading
Sigma-Prikry forcing I: The Axioms
Joint work with Alejandro Poveda and Dima Sinapova. Abstract. We introduce a class of notions of forcing which we call $\Sigma$-Prikry, and show that many of the known Prikry-type notions of forcing that centers around singular cardinals of countable cofinality … Continue reading
Inclusion modulo nonstationary
Joint work with Gabriel Fernandes and Miguel Moreno. Abstract. A classical theorem of Hechler asserts that the structure $\left(\omega^\omega,\le^*\right)$ is universal in the sense that for any $\sigma$-directed poset $\mathbb P$ with no maximal element, there is a ccc forcing … Continue reading
Partitioning a reflecting stationary set
Joint work with Maxwell Levine. Abstract. We address the question of whether a reflecting stationary set may be partitioned into two or more reflecting stationary subsets, providing various affirmative answers in ZFC. As an application to singular cardinals combinatorics, we infer … Continue reading
Souslin trees at successors of regular cardinals
Abstract. We present a weak sufficient condition for the existence of Souslin trees at successor of regular cardinals. The result is optimal and simultaneously improves an old theorem of Gregory and a more recent theorem of the author. Downloads: Citation … Continue reading
Posted in Publications, Souslin Hypothesis
Tagged Parameterized proxy principle, Souslin Tree
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Knaster and friends I: Closed colorings and precalibers
Joint work with Chris Lambie-Hanson. Abstract. The productivity of the $\kappa$-chain condition, where $\kappa$ is a regular, uncountable cardinal, has been the focus of a great deal of set-theoretic research. In the 1970s, consistent examples of $\kappa$-cc posets whose squares … Continue reading
