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