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Reflecting stationary set Commutative projection system HOD transformations Successor of Regular Cardinal Rainbow sets Absoluteness Vanishing levels Hindman's Theorem Erdos Cardinal Martin's Axiom approachability ideal Amenable C-sequence free Boolean algebra Axiom R Strongly compact cardinal polarized partition relation Prikry-type forcing stationary reflection Luzin set Forcing Axioms free Souslin tree Singular cofinality SNR coloring number Square-Brackets Partition Relations Subtle tree property Knaster and friends Prevalent singular cardinals Poset Commutative cancellative semigroups higher Baire space Iterated forcing Jonsson cardinal square principles stationary hitting Ramsey theory over partitions Open Access Chang's conjecture positive partition relation projective Boolean algebra AIM forcing Diamond for trees Precaliber b-scale indecomposable filter sap O-space PFA Diamond C-sequence Constructible Universe Selective Ultrafilter Foundations Rock n' Roll Diamond-sharp Singular cardinals combinatorics GMA Reduced Power Countryman line Small forcing Knaster Intersection model Postprocessing function Erdos-Hajnal graphs Ostaszewski square Non-saturation Cardinal function Hedetniemi's conjecture nonmeager set Sierpinski's onto mapping principle Almost-disjoint family Slim tree tensor product graph diamond star Strongly Luzin set Cohen real club_AD Forcing Subnormal ideal Lipschitz reduction Aronszajn tree Fast club Dushnik-Miller Dowker space Whitehead Problem Generalized Clubs Rado's conjecture Universal Sequences Ineffable cardinal Almost Souslin Local Club Condensation. Sakurai's Bell inequality Was Ulam right? reflection principles square Antichain Parameterized proxy principle Subadditive super-Souslin tree full tree Uniformization Analytic sets ZFC construction Subtle cardinal Uniformly coherent Cardinal Invariants Large Cardinals Fat stationary set 54G20 Strong coloring P-Ideal Dichotomy weak square Partition Relations Distributive tree Nonspecial tree OCA ccc middle diamond Uniformly homogeneous Greatly Mahlo Fodor-type reflection S-Space unbounded function Club Guessing Coherent tree Chromatic number Ulam matrix Sigma-Prikry Singular Density Filter reflection PFA(S)[S] weak diamond very good scale strongly bounded groups incompactness Respecting tree weak Kurepa tree Kurepa Hypothesis Well-behaved magma Closed coloring Mandelbrot set countably metacompact Shelah's Strong Hypothesis specializable Souslin tree regressive Souslin tree Souslin Tree stick Ascent Path Successor of Singular Cardinal Minimal Walks Generalized descriptive set theory L-space Hereditarily Lindelöf space xbox Microscopic Approach Almost countably chromatic Weakly compact cardinal
Author Archives: Assaf Rinot
A remark on Schimmerling’s question
Joint work with Ari Meir Brodsky. Abstract. Schimmerling asked whether
Weak square and stationary reflection
Joint work with Gunter Fuchs. Abstract. It is well-known that the square principle
Posted in Publications, Squares and Diamonds
Tagged 03E05, 03E35, 03E57, Diamond, Forcing Axioms, stationary reflection, weak square
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A strong form of König’s lemma
A student proposed to me the following strong form of König’s lemma: Conjecture. Suppose that
Posted in Blog
2 Comments
The 14th International Workshop on Set Theory in Luminy, October 2017
I gave an invited talk at the 14th International Workshop on Set Theory in Luminy in Marseille, October 2017. Talk Title: Distributive Aronszajn trees Abstract: It is well-known that that the statement “all
A forcing axiom deciding the generalized Souslin Hypothesis
Joint work with Chris Lambie-Hanson. Abstract. We derive a forcing axiom from the conjunction of square and diamond, and present a few applications, primary among them being the existence of super-Souslin trees. It follows that for every uncountable cardinal
Posted in Publications, Souslin Hypothesis
Tagged 03E05, 03E35, 03E57, Diamond, Forcing Axioms, Souslin Tree, square, super-Souslin tree
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6th European Set Theory Conference, July 2017
I gave a 3-lecture tutorial at the 6th European Set Theory Conference in Budapest, July 2017. Title: Strong colorings and their applications. Abstract. Consider the following questions. Is the product of two
Posted in Invited Talks, Open Problems
Tagged b-scale, Cohen real, Luzin set, Minimal Walks, Souslin Tree, Square-Brackets Partition Relations
4 Comments
Distributive Aronszajn trees
Joint work with Ari Meir Brodsky. Abstract. Ben-David and Shelah proved that if
ASL North American Meeting, March 2017
I gave a plenary talk at the 2017 ASL North American Meeting in Boise, March 2017. Talk Title: The current state of the Souslin problem. Abstract: Recall that the real line is that unique separable, dense linear ordering with no endpoints in … Continue reading
MFO workshop in Set Theory, February 2017
I gave an invited talk at the Set Theory workshop in Obwerwolfach, February 2017. Talk Title: Coloring vs. Chromatic. Abstract: In a joint work with Chris Lambie-Hanson, we study the interaction between compactness for the chromatic number (of graphs) and … Continue reading
Posted in Invited Talks
Tagged Chromatic number, coloring number, incompactness, stationary reflection
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The eightfold way
Joint work with James Cummings, Sy-David Friedman, Menachem Magidor, and Dima Sinapova. Abstract. Three central combinatorial properties in set theory are the tree property, the approachability property and stationary reflection. We prove the mutual independence of these properties by showing … Continue reading
