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