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Rock n' Roll Well-behaved magma Subtle cardinal positive partition relation weak square 54G20 higher Baire space Reduced Power Fast club super-Souslin tree Partition Relations Lipschitz reduction Almost Souslin Closed coloring Forcing with side conditions Uniformly coherent square Universal Sequences Postprocessing function Luzin set Slim tree Local Club Condensation. Open Access Axiom R diamond star Rado's conjecture S-Space Precaliber weak Kurepa tree Successor of Regular Cardinal Ostaszewski square free Souslin tree Large Cardinals projective Boolean algebra Cardinal Invariants Diamond-sharp GMA L-space Shelah's Strong Hypothesis Cohen real Ascent Path Commutative cancellative semigroups Mandelbrot set Entangled linear order Ulam matrix Distributive tree Countryman line stationary reflection unbounded function Fodor-type reflection Generalized descriptive set theory Hindman's Theorem Ramsey theory over partitions stationary hitting full tree Respecting tree Small forcing Greatly Mahlo incompactness Forcing approachability ideal Hereditarily Lindelöf space OCA Uniformly homogeneous Minimal Walks Fat stationary set reflection principles Jonsson cardinal AIM forcing Subadditive Hedetniemi's conjecture ccc Singular Density Dowker space Chromatic number transformations xbox Sakurai's Bell inequality PFA(S)[S] Uniformization Whitehead Problem Ineffable cardinal nonmeager set Martin's Axiom Dushnik-Miller Erdos-Hajnal graphs Cardinal function Partition relations for trees Filter reflection Singular cardinals combinatorics Ascending path polarized partition relation Antichain club_AD weak diamond free Boolean algebra Commutative projection system Strongly Luzin set ZFC construction Almost countably chromatic Sigma-Prikry strongly bounded groups Chang's conjecture Was Ulam right? Interval topology on trees Non-saturation Analytic sets Reflecting stationary set Rainbow sets square principles Aronszajn tree PFA Amenable C-sequence Prevalent singular cardinals C-sequence perfectly normal stick Strongly compact cardinal Strong coloring b-scale Knaster and friends Weakly compact cardinal Square-Brackets Partition Relations Subnormal ideal tensor product graph P-Ideal Dichotomy Diamond Erdos Cardinal Prikry-type forcing Parameterized proxy principle Intersection model HOD countably metacompact sap Iterated forcing Poset Nonspecial tree very good scale Diamond for trees indecomposable filter Successor of Singular Cardinal Absoluteness specializable Souslin tree regressive Souslin tree Subtle tree property Constructible Universe Almost-disjoint family Souslin Tree Singular cofinality Coherent tree Sierpinski's onto mapping principle Knaster Club Guessing O-space Kurepa Hypothesis coloring number Selective Ultrafilter SNR Forcing Axioms middle diamond Monotonically far Microscopic Approach Foundations Vanishing levels Generalized Clubs
Author Archives: Assaf Rinot
MFO workshop in Set Theory, April 2020
The Set Theory workshop in Obwerwolfach was supposed to take place April 2020, but was transformed into a webinar, due to COVID-19. Here you will find the title, abstract, slides and video of my webinar talk. Talk Title: Transformations of … Continue reading
Posted in Invited Talks
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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
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
The 15th International Workshop on Set Theory in Luminy, September 2019
I gave an invited talk at the 15th International Workshop on Set Theory in Luminy in Marseille, September 2019. Talk Title: Chain conditions, unbounded colorings and the C-sequence spectrum. Abstract: The productivity of the $\kappa$-chain condition, where $\kappa$ is a regular, … Continue reading
Posted in Invited Talks
Tagged Closed coloring, Knaster, Precaliber, stationary reflection, unbounded function
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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
