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Cohen real Hindman's Theorem Chang's conjecture Knaster and friends Nonspecial tree Prikry-type forcing Rainbow sets Open Access 54G20 Fat stationary set indecomposable ultrafilter full tree Rado's conjecture Forcing Axioms Lipschitz reduction Ramsey theory over partitions countably metacompact Dushnik-Miller super-Souslin tree approachability ideal SNR Amenable C-sequence Generalized descriptive set theory Subnormal ideal Slim tree Souslin Tree Hedetniemi's conjecture Mandelbrot set ZFC construction Aronszajn tree Erdos Cardinal transformations weak square Foundations Precaliber Diamond-sharp Knaster reflection principles Constructible Universe Iterated forcing sap diamond star Jonsson cardinal Whitehead Problem Uniformly coherent Dowker space Cardinal Invariants Reflecting stationary set Ascent Path square principles xbox Generalized Clubs Uniformly homogeneous stick Subtle tree property club_AD Small forcing incompactness Commutative cancellative semigroups Sierpinski's onto mapping principle Luzin set Parameterized proxy principle free Boolean algebra Sakurai's Bell inequality Intersection model Forcing Ulam matrix Uniformization Subtle cardinal P-Ideal Dichotomy Closed coloring Local Club Condensation. unbounded function Cardinal function ccc b-scale tensor product graph Singular cofinality Rock n' Roll stationary hitting Erdos-Hajnal graphs Selective Ultrafilter projective Boolean algebra weak Kurepa tree Universal Sequences Club Guessing coloring number Strongly compact cardinal positive partition relation Square-Brackets Partition Relations Hereditarily Lindelöf space S-Space Strongly Luzin set Diamond Coherent tree Subadditive C-sequence Ineffable cardinal Axiom R Microscopic Approach Chromatic number stationary reflection Successor of Singular Cardinal L-space Almost Souslin Almost-disjoint family Minimal Walks Fast club Vanishing levels GMA Was Ulam right? PFA Distributive tree Countryman line Prevalent singular cardinals Analytic sets Reduced Power Postprocessing function Non-saturation weak diamond very good scale Greatly Mahlo Fodor-type reflection Well-behaved magma Large Cardinals Singular Density Diamond for trees Poset strongly bounded groups Commutative projection system specializable Souslin tree Almost countably chromatic Absoluteness Singular cardinals combinatorics Successor of Regular Cardinal Weakly compact cardinal Respecting tree O-space Filter reflection Martin's Axiom free Souslin tree square Sigma-Prikry Ostaszewski square OCA polarized partition relation PFA(S)[S] AIM forcing middle diamond Strong coloring Kurepa Hypothesis HOD Antichain regressive Souslin tree nonmeager set Shelah's Strong Hypothesis Partition Relations higher Baire space
Tag Archives: xbox
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
Strongest transformations
Joint work with Jing Zhang. Abstract. We continue our study of maps transforming high-dimensional complicated objects into squares of stationary sets. Previously, we proved that many such transformations exist in ZFC, and here we address the consistency of the strongest … Continue reading
Posted in Partition Relations, Publications
Tagged Diamond, Minimal Walks, square, Square-Brackets Partition Relations, stick, transformations, xbox
2 Comments
A microscopic approach to Souslin-tree constructions. Part II
Joint work with Ari Meir Brodsky. Abstract. In Part I of this series, we presented the microscopic approach to Souslin-tree constructions, and argued that all known
More notions of forcing add a Souslin tree
Joint work with Ari Meir Brodsky. Abstract. An
Higher Souslin trees and the GCH, revisited
Abstract. It is proved that for every uncountable cardinal
Posted in Publications, Souslin Hypothesis
Tagged 03E05, 03E35, Open Access, regressive Souslin tree, Souslin Tree, square, Weakly compact cardinal, xbox
16 Comments
A microscopic approach to Souslin-tree constructions. Part I
Joint work with Ari Meir Brodsky. Abstract. We propose a parameterized proxy principle from which
Posted in Publications, Souslin Hypothesis
Tagged 03E05, 03E35, 03E65, 05C05, Coherent tree, Diamond, Microscopic Approach, Parameterized proxy principle, Slim tree, Souslin Tree, square, xbox
5 Comments
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
1 Comment
Square principles
Since the birth of Jensen’s original Square principle, many variations of the principle were introduced and intensively studied. Asaf Karagila suggested me today to put some order into all of these principles. Here is a trial. Definition. A square principle … Continue reading
