Archives
Keywords
Universal Sequences Well-behaved magma higher Baire space Sigma-Prikry Sierpinski's onto mapping principle incompactness Almost countably chromatic Singular Density Absoluteness Parameterized proxy principle Luzin set tensor product graph diamond star specializable Souslin tree Diamond-sharp Postprocessing function Ascent Path Almost Souslin reflection principles Souslin Tree free Souslin tree OCA ZFC construction Generalized Clubs Subadditive Subnormal ideal Axiom R strongly bounded groups Uniformization transformations Generalized descriptive set theory xbox Rainbow sets Small forcing L-space Fast club indecomposable ultrafilter super-Souslin tree SNR Kurepa Hypothesis approachability ideal positive partition relation full tree Erdos Cardinal Cohen real Selective Ultrafilter Reflecting stationary set C-sequence Vanishing levels Countryman line Sakurai's Bell inequality Jonsson cardinal PFA(S)[S] Iterated forcing GMA Amenable C-sequence Chang's conjecture 54G20 Diamond for trees Ostaszewski square Partition Relations Successor of Singular Cardinal Strong coloring Closed coloring Hindman's Theorem P-Ideal Dichotomy O-space Respecting tree middle diamond Commutative cancellative semigroups sap weak square Fat stationary set Intersection model Strongly Luzin set Uniformly coherent coloring number Martin's Axiom b-scale Cardinal Invariants PFA stick Prikry-type forcing Rado's conjecture Uniformly homogeneous Successor of Regular Cardinal S-Space Subtle tree property polarized partition relation Was Ulam right Analytic sets Distributive tree Knaster and friends Ineffable cardinal HOD Ulam matrix Square-Brackets Partition Relations Knaster Singular cofinality weak Kurepa tree Nonspecial tree Aronszajn tree Minimal Walks AIM forcing Constructible Universe projective Boolean algebra Dowker space square nonmeager set Greatly Mahlo Cardinal function Hereditarily Lindelöf space Almost-disjoint family Whitehead Problem Large Cardinals Subtle cardinal Weakly compact cardinal Commutative projection system countably metacompact Hedetniemi's conjecture free Boolean algebra Lipschitz reduction very good scale Rock n' Roll regressive Souslin tree Filter reflection Slim tree square principles Foundations Open Access Antichain Microscopic Approach Diamond Club Guessing Forcing Strongly compact cardinal club_AD Dushnik-Miller Poset ccc Local Club Condensation. Mandelbrot set Non-saturation Shelah's Strong Hypothesis Coherent tree Fodor-type reflection Ramsey theory over partitions Reduced Power Erdos-Hajnal graphs stationary hitting Singular cardinals combinatorics stationary reflection Prevalent singular cardinals unbounded function Chromatic number weak diamond Precaliber Forcing Axioms
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 $\kappa$-Souslin trees in a uniform way that does not … Continue reading
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 $\diamondsuit$-based constructions of Souslin trees with various additional properties may be rendered as applications of … Continue reading
More notions of forcing add a Souslin tree
Joint work with Ari Meir Brodsky. Abstract. An $\aleph_1$-Souslin tree is a complicated combinatorial object whose existence cannot be decided on the grounds of ZFC alone. But 15 years after Tennenbaum and independently Jech devised notions of forcing for introducing … Continue reading
Higher Souslin trees and the GCH, revisited
Abstract. It is proved that for every uncountable cardinal $\lambda$, GCH+$\square(\lambda^+)$ entails the existence of a $\text{cf}(\lambda)$-complete $\lambda^+$-Souslin tree. In particular, if GCH holds and there are no $\aleph_2$-Souslin trees, then $\aleph_2$ is weakly compact in Godel’s constructible universe, improving … Continue reading
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 $\kappa$-Souslin trees with various additional features can be constructed, regardless of the identity of $\kappa$. We then introduce the microscopic approach, which is a simple … Continue reading
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 $L$ for every infinite cardinal. As an application, we prove that … Continue reading
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
