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Axiom R Prikry-type forcing Erdos-Hajnal graphs Uniformly homogeneous Amenable C-sequence Constructible Universe Successor of Singular Cardinal Chang's conjecture positive partition relation Dowker space strongly bounded groups Singular cardinals combinatorics Selective Ultrafilter b-scale Commutative projection system Antichain Luzin set stationary hitting Ostaszewski square Small forcing Was Ulam right? Foundations Strongly compact cardinal Generalized Clubs Absoluteness Cardinal Invariants Respecting tree PFA(S)[S] full tree Closed coloring Erdos Cardinal Iterated forcing Subtle tree property Rainbow sets Singular cofinality Subtle cardinal Precaliber Uniformly coherent C-sequence Non-saturation incompactness Hereditarily Lindelöf space Greatly Mahlo square xbox Subnormal ideal Hedetniemi's conjecture Subadditive Minimal Walks Countryman line Dushnik-Miller very good scale weak diamond free Boolean algebra countably metacompact Square-Brackets Partition Relations AIM forcing Fodor-type reflection approachability ideal SNR square principles higher Baire space transformations Parameterized proxy principle Fast club Rock n' Roll Lipschitz reduction Shelah's Strong Hypothesis Weakly compact cardinal super-Souslin tree Poset Nonspecial tree S-Space L-space Postprocessing function Knaster and friends O-space Ramsey theory over partitions Prevalent singular cardinals polarized partition relation tensor product graph Club Guessing Diamond for trees nonmeager set free Souslin tree Diamond-sharp Almost Souslin Uniformization Cardinal function regressive Souslin tree Slim tree weak square Open Access stationary reflection coloring number Commutative cancellative semigroups Partition Relations Rado's conjecture projective Boolean algebra Strongly Luzin set Hindman's Theorem HOD Kurepa Hypothesis Sakurai's Bell inequality Distributive tree club_AD Cohen real ccc Chromatic number Reflecting stationary set Ineffable cardinal Well-behaved magma weak Kurepa tree 54G20 Ascent Path unbounded function stick Ulam matrix specializable Souslin tree Analytic sets Forcing Local Club Condensation. Coherent tree Jonsson cardinal Large Cardinals Whitehead Problem Fat stationary set Forcing Axioms Universal Sequences Sierpinski's onto mapping principle OCA PFA Generalized descriptive set theory Almost-disjoint family Martin's Axiom ZFC construction Vanishing levels Knaster Mandelbrot set reflection principles Strong coloring Souslin Tree Sigma-Prikry Reduced Power P-Ideal Dichotomy GMA Singular Density indecomposable filter middle diamond Microscopic Approach Aronszajn tree Almost countably chromatic Successor of Regular Cardinal sap Intersection model Diamond diamond star Filter reflection
Author Archives: Assaf Rinot
Square with built-in diamond-plus
Joint work with Ralf Schindler. Abstract. We formulate combinatorial principles that combine the square principle with various strong forms of diamond, and prove that the strongest amongst them holds in
Posted in Publications, Squares and Diamonds
Tagged 03E05, 03E45, Almost Souslin, diamond star, Kurepa Hypothesis, Minimal Walks, Respecting tree, square, xbox
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P.O.I. Workshop in pure and descriptive set theory, September 2015
I gave an invited talk at the P.O.I Workshop in pure and descriptive set theory, Torino, September 26, 2015. Title:
Reduced powers of Souslin trees
Joint work with Ari Meir Brodsky. Abstract. We study the relationship between a
The Apter-Gitik birthday conference, May 2015
I give an invited (blackboard) talk at the Apter-Gitik birthday conference, Carnegie Mellon University, May 30-31 2015. Title: Putting a diamond inside the square. Abstract: By a 35-year-old theorem of Shelah,
Posted in Invited Talks
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Forcing and its Applications Retrospective Workshop, April 2015
I gave an invited talk at Forcing and its Applications Retrospective Workshop, Toronto, April 1st, 2015. Title: A microscopic approach to Souslin trees constructions Abstract: We present an approach to construct
Posted in Invited Talks
Tagged Microscopic Approach, Parameterized proxy principle, Souslin Tree
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Putting a diamond inside the square
Abstract. By a 35-year-old theorem of Shelah,
Posted in Publications, Squares and Diamonds
Tagged 03E05, 03E45, Diamond, square, Successor of Singular Cardinal
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Generalizations of Martin’s Axiom and the well-met condition
Recall that Martin’s Axiom asserts that for every partial order
Many diamonds from just one
Recall Jensen’s diamond principle over a stationary subset
Same Graph, Different Universe
Abstract. May the same graph admit two different chromatic numbers in two different universes? how about infinitely many different values? and can this be achieved without changing the cardinals structure? In this paper, it is proved that in Godel’s constructible … Continue reading
Posted in Infinite Graphs, Publications
Tagged 03E35, 05C15, 05C63, approachability ideal, Chromatic number, Constructible Universe, Forcing, Ostaszewski square
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