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Coherent tree super-Souslin tree club_AD C-sequence strongly bounded groups indecomposable filter Diamond Foundations Successor of Singular Cardinal Sakurai's Bell inequality Prevalent singular cardinals Knaster and friends ZFC construction Constructible Universe Reduced Power Universal Sequences Absoluteness Ineffable cardinal Chromatic number polarized partition relation Filter reflection Hedetniemi's conjecture Selective Ultrafilter Non-saturation positive partition relation Local Club Condensation. Analytic sets Kurepa Hypothesis Greatly Mahlo Monotonically far stationary hitting Diamond for trees PFA(S)[S] Reflecting stationary set Almost countably chromatic Hereditarily Lindelöf space Partition relations for trees Entangled linear order Partition Relations Amenable C-sequence Slim tree weak Kurepa tree square principles Ramsey theory over partitions Antichain Ascending path approachability ideal Dowker space countably metacompact SNR Commutative cancellative semigroups Martin's Axiom Iterated forcing higher Baire space Cardinal function Small forcing coloring number GMA Countryman line Fast club ccc P-Ideal Dichotomy Axiom R Dushnik-Miller Prikry-type forcing Luzin set PFA Aronszajn tree xbox Rainbow sets Erdos Cardinal transformations Well-behaved magma b-scale 54G20 projective Boolean algebra Successor of Regular Cardinal Club Guessing nonmeager set Forcing very good scale HOD Precaliber Singular cardinals combinatorics incompactness Shelah's Strong Hypothesis O-space Sierpinski's onto mapping principle Ascent Path Strongly compact cardinal Open Access Whitehead Problem Distributive tree Generalized descriptive set theory Uniformly coherent Nonspecial tree Subnormal ideal Subtle cardinal Mandelbrot set diamond star free Souslin tree Generalized Clubs Respecting tree S-Space weak diamond AIM forcing Square-Brackets Partition Relations Diamond-sharp unbounded function sap Forcing with side conditions Commutative projection system Strongly Luzin set Singular Density Subtle tree property square free Boolean algebra Microscopic Approach Strong coloring Closed coloring specializable Souslin tree Sigma-Prikry Singular cofinality Was Ulam right? Almost Souslin reflection principles Cardinal Invariants middle diamond Knaster Poset Jonsson cardinal full tree Ostaszewski square perfectly normal regressive Souslin tree Cohen real stationary reflection stick Postprocessing function Erdos-Hajnal graphs Ulam matrix Fat stationary set Uniformly homogeneous Forcing Axioms weak square Vanishing levels Souslin Tree Weakly compact cardinal Minimal Walks Parameterized proxy principle Fodor-type reflection Almost-disjoint family Rado's conjecture Subadditive Intersection model tensor product graph Uniformization Large Cardinals Chang's conjecture Lipschitz reduction L-space Rock n' Roll Hindman's Theorem Interval topology on trees OCA
Author Archives: Assaf Rinot
Partition relations for trees I: Incomparable trees
Joint work with Tanmay Inamdar. Abstract. Todorcevic proved that Martin’s axiom implies that every two coherent $\aleph_1$-Aronszajn trees are comparable. Here, from cardinal arithmetic assumptions, we obtain the failure of the analogous statement for higher trees. In particular, for every … Continue reading
Posted in Partition Relations, Preprints
Tagged Lipschitz reduction, Partition relations for trees
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RIMS workshop on Set Theory 2025
I gave an online contributed talk at the RIMS workshop on Set Theory 2025 in Kyoto, December 2025. Talk Title: What is a higher forcing axiom? Abstract: There are multiple interpretations of what is a forcing axiom. We shall survey … Continue reading
The 18th International Workshop on Set Theory in Luminy, November 2015
I gave an invited talk at the 18th International Workshop on Set Theory in Luminy in Marseille, November 2025. Talk Title: What is a higher forcing axiom? Abstract: There are multiple interpretations of what is a forcing axiom. We shall … Continue reading
Posted in Invited Talks
Tagged Forcing Axioms
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Conference in honor of Saharon Shelah’s 80th birthday
I gave an invited talk at the conference in honor of Shelah’s 80th birthday, July 2025. Talk Title: Marginalia to [Sh:365] Abstract: Solovay famously proved that every stationary subset of a regular uncountable cardinal kappa may be decomposed into kappa … Continue reading
Posted in Invited Talks
Tagged Greatly Mahlo, Strong coloring, Was Ulam right?
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2025 Annual conference of the IMU
I gave an invited talk at the Set Theory session of the annual meeting of the IMU, July 2025. Talk Title: What my co-authors taught me about indecomposability Abstract: Ulam’s measure problem studies when there is a countably-additive two-valued measure … Continue reading
Posted in Invited Talks
Tagged indecomposable filter
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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
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
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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
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
2 Comments
