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Absoluteness Sigma-Prikry Subadditive Hedetniemi's conjecture Analytic sets Coherent tree Knaster and friends transformations Knaster Uniformly homogeneous HOD Fast club Square-Brackets Partition Relations Local Club Condensation. Postprocessing function OCA Ramsey theory over partitions coloring number S-Space Distributive tree Chromatic number SNR Diamond-sharp Dowker space Non-saturation O-space AIM forcing tensor product graph Shelah's Strong Hypothesis nonmeager set Strongly Luzin set Dushnik-Miller Slim tree incompactness Rado's conjecture Souslin Tree Mandelbrot set Vanishing levels Amenable C-sequence Foundations Fat stationary set L-space square diamond star polarized partition relation countably metacompact Uniformization Precaliber Almost-disjoint family Commutative cancellative semigroups Erdos-Hajnal graphs stationary hitting Forcing Axioms Ulam matrix Hereditarily Lindelöf space Weakly compact cardinal Axiom R Well-behaved magma Reflecting stationary set Aronszajn tree free Souslin tree Subnormal ideal positive partition relation weak Kurepa tree Strong coloring very good scale Luzin set Whitehead Problem Prikry-type forcing GMA Poset Large Cardinals PFA stick Club Guessing ccc Microscopic Approach Rock n' Roll b-scale Ineffable cardinal Minimal Walks Generalized Clubs Cardinal function Partition Relations Erdos Cardinal regressive Souslin tree middle diamond Ostaszewski square Ascent Path Successor of Regular Cardinal Small forcing unbounded function Subtle tree property C-sequence Was Ulam right Almost Souslin Forcing Nonspecial tree Singular cardinals combinatorics Cardinal Invariants P-Ideal Dichotomy weak diamond 54G20 Closed coloring ZFC construction Open Access PFA(S)[S] sap Fodor-type reflection Cohen real Diamond Generalized descriptive set theory Iterated forcing Constructible Universe Chang's conjecture reflection principles Kurepa Hypothesis approachability ideal Jonsson cardinal Singular Density Sierpinski's onto mapping principle xbox Greatly Mahlo projective Boolean algebra Filter reflection Reduced Power specializable Souslin tree Antichain club_AD Universal Sequences Uniformly coherent square principles full tree Lipschitz reduction Rainbow sets indecomposable ultrafilter free Boolean algebra Diamond for trees Selective Ultrafilter Almost countably chromatic Prevalent singular cardinals Sakurai's Bell inequality higher Baire space strongly bounded groups super-Souslin tree stationary reflection weak square Successor of Singular Cardinal Martin's Axiom Subtle cardinal Parameterized proxy principle Singular cofinality Hindman's Theorem
Author Archives: Assaf Rinot
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
50 Years of Set Theory in Toronto, May 2019
I gave an invited talk at the 50 Years of Set Theory in Toronto meeting, Fields Institute for Research in Mathematical Sciences, May 2019. Talk Title: Analytic quasi-orders and two forms of diamond Abstract: We study Borel reduction of equivalence relations … Continue reading
Posted in Invited Talks
Tagged Analytic sets, Diamond-sharp, Generalized descriptive set theory
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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
4th Arctic Set Theory Workshop, January 2019
I gave an invited talk at the Arctic Set Theory Workshop 4 in Kilpisjärvi, January 2019. Talk Title: Splitting a stationary set: Is there another way? Abstract: Motivated by a problem in pcf theory, we seek for a new way … Continue reading
Posted in Invited Talks
Tagged Club Guessing, Reflecting stationary set, Ulam matrix, very good scale
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