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Closed coloring Lipschitz reduction Uniformly coherent Well-behaved magma Interval topology on trees Hereditarily Lindelöf space PFA higher Baire space Almost Souslin L-space stick Shelah's Strong Hypothesis Successor of Regular Cardinal Subtle cardinal Postprocessing function middle diamond very good scale Precaliber Knaster and friends transformations Fat stationary set Iterated forcing unbounded function square Cardinal function Whitehead Problem Mandelbrot set Uniformly homogeneous Almost countably chromatic Fast club Prikry-type forcing Forcing Axioms sap Poset Forcing with side conditions strongly bounded groups Hindman's Theorem HOD Weakly compact cardinal Constructible Universe Microscopic Approach tensor product graph Sakurai's Bell inequality reflection principles S-Space Greatly Mahlo ccc Sierpinski's onto mapping principle Non-saturation Singular cardinals combinatorics xbox Commutative cancellative semigroups O-space Monotonically far Minimal Walks Commutative projection system Local Club Condensation. Generalized Clubs specializable Souslin tree Entangled linear order Rock n' Roll Selective Ultrafilter Reflecting stationary set Rado's conjecture SNR Almost-disjoint family Universal Sequences C-sequence Antichain Ascent Path polarized partition relation club_AD free Souslin tree weak square stationary hitting Open Access Slim tree Strongly Luzin set nonmeager set Countryman line Generalized descriptive set theory Amenable C-sequence Ascending path Filter reflection Was Ulam right? Respecting tree Jonsson cardinal P-Ideal Dichotomy Nonspecial tree Square-Brackets Partition Relations 54G20 diamond star Diamond Successor of Singular Cardinal Cohen real Subnormal ideal Dowker space Uniformization weak Kurepa tree Strongly compact cardinal Hedetniemi's conjecture Fodor-type reflection Singular cofinality perfectly normal Ineffable cardinal Dushnik-Miller Cardinal Invariants regressive Souslin tree Martin's Axiom Souslin Tree Prevalent singular cardinals ZFC construction Luzin set Knaster Erdos Cardinal Large Cardinals Erdos-Hajnal graphs Foundations weak diamond Kurepa Hypothesis Partition Relations Strong coloring Forcing Coherent tree Rainbow sets Small forcing square principles OCA Subadditive Reduced Power Diamond-sharp Diamond for trees indecomposable filter incompactness super-Souslin tree projective Boolean algebra Singular Density Distributive tree countably metacompact full tree positive partition relation Vanishing levels Intersection model Ramsey theory over partitions approachability ideal stationary reflection PFA(S)[S] Partition relations for trees Ostaszewski square Subtle tree property AIM forcing Chang's conjecture Absoluteness free Boolean algebra Aronszajn tree Ulam matrix GMA coloring number Chromatic number b-scale Axiom R Club Guessing Parameterized proxy principle Sigma-Prikry Analytic sets
Author Archives: Assaf Rinot
Partition relations for trees II: Entangled linear orders
Joint work with Tanmay Inamdar. Abstract. We find new sufficient conditions for the existence of entangled linear orders. The constructions use anti-Ramsey colourings for trees, and they provide a fine control on the extent of entangledness. As an application, from … Continue reading
Posted in Partition Relations, Preprints
Tagged Aronszajn tree, Entangled linear order, Partition relations for trees, Strongly Luzin set
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More notions of forcing add a square
Joint work with Yair Hayut and Zhixing You. Abstract. Foreman and Magidor showed that the continuum hypothesis implies the existence of a countably-closed $\aleph_2$-cc forcing notion $\mathbb P$ for adding $\square_{\omega_1}$. Here, we show that $\mathbb P$ may consistently be … Continue reading
Posted in Squares and Diamonds
Tagged full tree, Souslin Tree, square principles, super-Souslin tree
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40th summer conference on topology and its applications
I gave an invited talk at the General and Set-Theoretic Topology session of the 40th summer conference on topology and its applications, July 2026. Talk title: A tree-based perfectly normal space whose square is not countably metacompact. Abstract. The study … Continue reading
Posted in Invited Talks, Topology
Tagged Interval topology on trees
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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, Publications
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
