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Club Guessing Rock n' Roll Universal Sequences Local Club Condensation. Subnormal ideal Fat stationary set Almost countably chromatic Interval topology on trees Sigma-Prikry Countryman line Closed coloring xbox Jonsson cardinal Poset Hedetniemi's conjecture positive partition relation Ascent Path coloring number Whitehead Problem Shelah's Strong Hypothesis Almost-disjoint family Erdos Cardinal indecomposable filter Almost Souslin Generalized Clubs Slim tree Absoluteness S-Space Hindman's Theorem Non-saturation Luzin set incompactness regressive Souslin tree stationary hitting Aronszajn tree SNR Square-Brackets Partition Relations very good scale strongly bounded groups stationary reflection super-Souslin tree weak diamond Axiom R Foundations Fodor-type reflection Microscopic Approach Selective Ultrafilter OCA Singular Density Cohen real polarized partition relation Diamond Respecting tree Strong coloring stick Knaster Partition relations for trees weak Kurepa tree Ramsey theory over partitions Singular cardinals combinatorics Cardinal Invariants Constructible Universe Forcing b-scale HOD Successor of Singular Cardinal Parameterized proxy principle Diamond-sharp Prevalent singular cardinals diamond star Partition Relations Rado's conjecture square principles Chromatic number transformations Ostaszewski square Commutative projection system Ascending path Precaliber L-space Cardinal function projective Boolean algebra Coherent tree Uniformization free Souslin tree middle diamond Uniformly homogeneous Souslin Tree Forcing Axioms Generalized descriptive set theory C-sequence Postprocessing function Vanishing levels Successor of Regular Cardinal Analytic sets Minimal Walks Sakurai's Bell inequality PFA(S)[S] Singular cofinality Dowker space Kurepa Hypothesis Reflecting stationary set Knaster and friends Martin's Axiom full tree AIM forcing Nonspecial tree Well-behaved magma higher Baire space Distributive tree Diamond for trees Amenable C-sequence tensor product graph Strongly compact cardinal Reduced Power 54G20 Greatly Mahlo Mandelbrot set Filter reflection Prikry-type forcing Sierpinski's onto mapping principle Monotonically far PFA Large Cardinals Entangled linear order Antichain Was Ulam right? Intersection model sap perfectly normal specializable Souslin tree Strongly Luzin set O-space approachability ideal countably metacompact Erdos-Hajnal graphs Subtle tree property weak square unbounded function ccc Weakly compact cardinal Ineffable cardinal Rainbow sets P-Ideal Dichotomy Ulam matrix Commutative cancellative semigroups ZFC construction Hereditarily Lindelöf space reflection principles Chang's conjecture nonmeager set Open Access GMA Subtle cardinal free Boolean algebra Lipschitz reduction club_AD Uniformly coherent Subadditive Small forcing Forcing with side conditions Fast club Iterated forcing square Dushnik-Miller
Author Archives: Assaf Rinot
A new model for all C-sequences are trivial
Joint work with Zhixing You and Jiachen Yuan. Abstract. We construct a model in which all C-sequences are trivial, yet there exists a $\kappa$-Souslin tree with full vanishing levels. This answers a question from a previous paper, and provides an … Continue reading
Posted in Compactness, Publications
Tagged Ascent Path, C-sequence, Intersection model, Souslin Tree, Subtle tree property, Vanishing levels
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MFO workshop in Set Theory, January 2025
I gave an invited talk at the Set Theory meeting in Obwerwolfach, January 2025. Talk Title: Non-structure theorems for higher Aronszajn lines. Abstract: An $\omega_1$-Countryman line is an uncountable linear order $L$ such that $L^2$ (with the pointwise ordering) is … Continue reading
Posted in Invited Talks
Tagged Countryman line, Monotonically far
Comments Off on MFO workshop in Set Theory, January 2025
Walks on uncountable ordinals and non-structure theorems for higher Aronszajn lines
Joint work with Tanmay Inamdar. Abstract. We investigate global structural properties of linear orders of a fixed infinite size. It is classical that the countable linear orders and the continuum-sized orders exhibit contrasting behaviours. Modern results show that strong extensions … Continue reading
Posted in Basis problems, Partition Relations, Preprints
Tagged Aronszajn tree, Ascending path, Club Guessing, Countryman line, Entangled linear order, Minimal Walks, Monotonically far, Partition relations for trees, Strong coloring, Subtle tree property, Vanishing levels, ZFC construction
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Ketonen’s question and other cardinal sins
Joint work with Zhixing You and Jiachen Yuan. Abstract. Answering a question of Ketonen from the late 1970’s, it is proved that a weakly compact cardinal carrying an indecomposable ultrafilter need not be measurable. The result is obtained by analyzing … Continue reading
120 Years of Choice, July 2024
I gave an invited talk at the 120 Years of Choice conference, July 2024. Talk Title: Mathematician’s best friend Abstract: Jensen’s diamond is a very useful postulate. It is well-known that it implies the continuum hypothesis, that it is equivalent … Continue reading
Diamond on Kurepa trees
Joint work with Ziemek Kostana and Saharon Shelah. Abstract. We introduce a new weak variation of diamond that is meant to guess only the branches of a Kurepa tree. We demonstrate that this variation is considerably weaker than diamond by … Continue reading
Proxy principles in combinatorial set theory
Joint work with Ari Meir Brodsky and Shira Yadai. Abstract. The parameterized proxy principles were introduced by Brodsky and Rinot in a 2017 paper as new foundations for the construction of $\kappa$-Souslin trees in a uniform way that does not … Continue reading
Squares, ultrafilters and forcing axioms
Joint work with Chris Lambie-Hanson and Jing Zhang. Abstract. We study the interplay of the three families of combinatorial objects or principles. Specifically, we show the following. Strong forcing axioms, in general incompatible with the existence of indexed squares, can … Continue reading
May the successor of a singular cardinal be Jonsson?
Abstract: Whether the successor of a singular cardinal can be Jónsson is a very old and famous open problem in set theory. Here, we collect necessary conditions for an affirmative answer, and put forward a list of closely-related questions in … Continue reading
Posted in Open Problems, Singular Cardinals Combinatorics
Tagged Jonsson cardinal, Open Access
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