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Greatly Mahlo Uniformization Uniformly homogeneous Diamond for trees Ulam matrix Sakurai's Bell inequality GMA Diamond reflection principles stick Subtle tree property Rado's conjecture Square-Brackets Partition Relations Minimal Walks Reflecting stationary set Commutative projection system projective Boolean algebra Subnormal ideal ZFC construction Lipschitz reduction Filter reflection Hedetniemi's conjecture xbox Respecting tree indecomposable filter Microscopic Approach Knaster and friends Large Cardinals Distributive tree Analytic sets strongly bounded groups specializable Souslin tree stationary reflection Sierpinski's onto mapping principle sap Generalized descriptive set theory Parameterized proxy principle Almost countably chromatic Cardinal function Iterated forcing Constructible Universe Almost-disjoint family Singular cofinality square S-Space Club Guessing Chromatic number Poset PFA Subadditive Slim tree Martin's Axiom super-Souslin tree middle diamond full tree Strong coloring Successor of Regular Cardinal O-space Souslin Tree OCA Small forcing Generalized Clubs Non-saturation Local Club Condensation. Commutative cancellative semigroups 54G20 SNR Open Access Aronszajn tree Dowker space Reduced Power Ineffable cardinal diamond star approachability ideal Ascent Path b-scale Vanishing levels polarized partition relation Erdos-Hajnal graphs regressive Souslin tree Whitehead Problem Was Ulam right? Rock n' Roll Antichain Foundations unbounded function HOD very good scale PFA(S)[S] Erdos Cardinal Nonspecial tree positive partition relation countably metacompact Prevalent singular cardinals Diamond-sharp Countryman line Luzin set P-Ideal Dichotomy square principles AIM forcing Weakly compact cardinal Partition Relations Entangled family Fast club Postprocessing function weak diamond Hereditarily Lindelöf space Shelah's Strong Hypothesis Universal Sequences Well-behaved magma Forcing Axioms Amenable C-sequence Sigma-Prikry Closed coloring Strongly compact cardinal Chang's conjecture Rainbow sets Cohen real Monotonically far Knaster Dushnik-Miller C-sequence Selective Ultrafilter L-space Successor of Singular Cardinal weak Kurepa tree Cardinal Invariants Forcing Hindman's Theorem Axiom R transformations Strongly Luzin set Precaliber Singular cardinals combinatorics incompactness free Souslin tree club_AD Jonsson cardinal ccc Uniformly coherent Ostaszewski square Subtle cardinal Intersection model Fodor-type reflection higher Baire space tensor product graph Mandelbrot set coloring number free Boolean algebra Kurepa Hypothesis stationary hitting nonmeager set Coherent tree Ramsey theory over partitions Prikry-type forcing Singular Density weak square Absoluteness Fat stationary set Almost Souslin
Author Archives: Assaf Rinot
Was Ulam right? III: Indecomposable ideals
Joint work with Tanmay Inamdar. Abstract. We continue our study of Ulam’s measure problem. In contrast to our previous works, we shift our focus from measures stratified by their additivity, to measures stratified by their indecomposability. The breakthrough here is … Continue reading
Posted in Partition Relations, Preprints
Tagged indecomposable filter, Minimal Walks, Non-saturation, Partition Relations, Sierpinski's onto mapping principle, Ulam matrix, Was Ulam right?
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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
Posted in Compactness, Preprints
Tagged Ascent Path, C-sequence, Intersection model, Souslin Tree, 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
Posted in Invited Talks
Tagged Countryman line, Monotonically far
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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
Ketonen’s question and other cardinal sins
Joint work with Zhixing You and Jiachen Yuan. Abstract. Intersection models of generic extensions obtained from a commutative projection systems of notions of forcing has recently regained interest, especially in the study of descriptive set theory. Here, we show that … Continue reading
Posted in Compactness, Preprints
Tagged 03E05, 03E35, 03E55, Ascent Path, C-sequence, Commutative projection system, indecomposable filter, Intersection model, Strongly compact cardinal
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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 only guess the branches of a Kurepa tree. We demonstrate that this variation is considerably weaker than diamond by … Continue reading
Posted in Preprints, Squares and Diamonds
Tagged Diamond, Diamond for trees, Iterated forcing, Kurepa Hypothesis, weak Kurepa tree
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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
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
Posted in Compactness, Publications
Tagged Forcing Axioms, indecomposable filter, Subadditive, unbounded function
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