Archives
Keywords
Ulam matrix Filter reflection Uniformization Distributive tree P-Ideal Dichotomy unbounded function Martin's Axiom Entangled linear order S-Space indecomposable filter Fat stationary set Interval topology on trees stationary hitting Shelah's Strong Hypothesis square principles Sierpinski's onto mapping principle middle diamond Cardinal function sap Coherent tree Partition relations for trees Rock n' Roll Prikry-type forcing Nonspecial tree Absoluteness Hedetniemi's conjecture Parameterized proxy principle Diamond for trees countably metacompact Knaster and friends Universal Sequences Generalized descriptive set theory reflection principles Strongly Luzin set Open Access Analytic sets super-Souslin tree Knaster Diamond Kurepa Hypothesis Subadditive ccc Ineffable cardinal Aronszajn tree Singular cofinality Uniformly homogeneous Generalized Clubs Forcing Reflecting stationary set Dushnik-Miller Large Cardinals Microscopic Approach positive partition relation club_AD Weakly compact cardinal Dowker space strongly bounded groups Partition Relations stationary reflection nonmeager set Singular Density very good scale Fodor-type reflection Cardinal Invariants PFA Iterated forcing Constructible Universe Luzin set Rado's conjecture weak Kurepa tree Local Club Condensation. weak square xbox tensor product graph Mandelbrot set Postprocessing function projective Boolean algebra Square-Brackets Partition Relations Foundations Countryman line stick Small forcing transformations Singular cardinals combinatorics Closed coloring Sigma-Prikry Well-behaved magma Successor of Singular Cardinal Antichain Ramsey theory over partitions Erdos Cardinal Successor of Regular Cardinal Jonsson cardinal Uniformly coherent AIM forcing Greatly Mahlo Almost Souslin Monotonically far approachability ideal L-space OCA Amenable C-sequence regressive Souslin tree PFA(S)[S] incompactness Chromatic number Erdos-Hajnal graphs Poset SNR b-scale Lipschitz reduction Commutative projection system Rainbow sets full tree O-space Subtle tree property Cohen real diamond star Ascending path Ostaszewski square Subtle cardinal coloring number Strong coloring Slim tree Vanishing levels Sakurai's Bell inequality Strongly compact cardinal Chang's conjecture square Respecting tree higher Baire space Forcing with side conditions GMA Intersection model Reduced Power Selective Ultrafilter Club Guessing Almost countably chromatic Whitehead Problem specializable Souslin tree Commutative cancellative semigroups Subnormal ideal free Boolean algebra Non-saturation Axiom R perfectly normal Souslin Tree Ascent Path Minimal Walks C-sequence Prevalent singular cardinals free Souslin tree HOD Was Ulam right? Forcing Axioms weak diamond Fast club 54G20 Almost-disjoint family Hindman's Theorem Hereditarily Lindelöf space Precaliber Diamond-sharp polarized partition relation ZFC construction
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
1 Comment
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
