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approachability ideal Foundations Generalized Clubs Diamond Partition Relations regressive Souslin tree Prikry-type forcing Constructible Universe Sierpinski's onto mapping principle Commutative projection system strongly bounded groups Dowker space Entangled linear order Universal Sequences Slim tree Coherent tree Local Club Condensation. Respecting tree Nonspecial tree Strongly Luzin set nonmeager set Kurepa Hypothesis Diamond for trees Intersection model Fast club tensor product graph Diamond-sharp free Boolean algebra b-scale countably metacompact Luzin set Rock n' Roll Knaster Dushnik-Miller PFA Almost-disjoint family Strongly compact cardinal Rainbow sets Singular cardinals combinatorics GMA AIM forcing Parameterized proxy principle Antichain ZFC construction Precaliber Cohen real Ascending path Uniformly coherent Knaster and friends stationary reflection SNR diamond star Ineffable cardinal HOD Almost Souslin S-Space Non-saturation Sigma-Prikry Hereditarily Lindelöf space square principles Forcing Axioms Postprocessing function Countryman line Vanishing levels C-sequence 54G20 unbounded function Almost countably chromatic full tree Ramsey theory over partitions Jonsson cardinal Singular Density Monotonically far Cardinal function Partition relations for trees transformations Forcing specializable Souslin tree Reflecting stationary set stationary hitting stick Axiom R Chang's conjecture Reduced Power Erdos-Hajnal graphs perfectly normal Small forcing Souslin Tree Fat stationary set ccc O-space P-Ideal Dichotomy Ulam matrix Generalized descriptive set theory weak Kurepa tree Whitehead Problem Distributive tree Square-Brackets Partition Relations OCA Open Access Iterated forcing Mandelbrot set Analytic sets Microscopic Approach reflection principles Rado's conjecture Uniformization Interval topology on trees Uniformly homogeneous Closed coloring square Successor of Singular Cardinal Selective Ultrafilter positive partition relation PFA(S)[S] Shelah's Strong Hypothesis xbox coloring number Weakly compact cardinal Hindman's Theorem very good scale Poset Erdos Cardinal club_AD Greatly Mahlo incompactness indecomposable filter Subtle tree property Sakurai's Bell inequality super-Souslin tree polarized partition relation Ostaszewski square higher Baire space Successor of Regular Cardinal Commutative cancellative semigroups Hedetniemi's conjecture Fodor-type reflection sap Club Guessing free Souslin tree Well-behaved magma L-space Aronszajn tree middle diamond Singular cofinality Cardinal Invariants Ascent Path Prevalent singular cardinals Lipschitz reduction Subtle cardinal Amenable C-sequence weak square Chromatic number Subnormal ideal Absoluteness Martin's Axiom Subadditive Large Cardinals Filter reflection weak diamond Minimal Walks Strong coloring projective Boolean algebra Forcing with side conditions Was Ulam right?
Author Archives: Assaf Rinot
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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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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11th Young Set Theory Workshop, June 2018
I gave a 4-lecture tutorial at the 11th Young Set Theory Workshop, Lausanne, June 2018. Title: In praise of C-sequences. Abstract. Ulam and Solovay showed that any stationary set may be split into two. Is it also the case that … Continue reading
Posted in Invited Talks
Tagged Aronszajn tree, C-sequence, incompactness, Knaster, Minimal Walks, Postprocessing function, square
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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
A remark on Schimmerling’s question
Joint work with Ari Meir Brodsky. Abstract. Schimmerling asked whether $\square^*_\lambda$ together with GCH entails the existence of a $\lambda^+$-Souslin tree, for a singular cardinal $\lambda$. Here, we provide an affirmative answer under the additional assumption that there exists a … Continue reading
