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Axiom R Non-saturation Hindman's Theorem Dowker space Subadditive Diamond Aronszajn tree Nonspecial tree Constructible Universe Generalized descriptive set theory Weakly compact cardinal Rock n' Roll weak diamond Ulam matrix Analytic sets Generalized Clubs Chromatic number Subnormal ideal Singular Density Mandelbrot set Partition Relations Absoluteness coloring number Fat stationary set Sierpinski's onto mapping principle Rado's conjecture Lipschitz reduction Greatly Mahlo C-sequence regressive Souslin tree Universal Sequences weak square Almost Souslin square principles ZFC construction Large Cardinals free Souslin tree xbox Knaster O-space stationary reflection Small forcing Rainbow sets Fast club Jonsson cardinal Reflecting stationary set unbounded function sap Minimal Walks Well-behaved magma very good scale Iterated forcing incompactness Local Club Condensation. projective Boolean algebra Parameterized proxy principle Prevalent singular cardinals Closed coloring Square-Brackets Partition Relations super-Souslin tree Hereditarily Lindelöf space Distributive tree Ascent Path Uniformly coherent Subtle cardinal AIM forcing polarized partition relation Souslin Tree Successor of Singular Cardinal Cohen real higher Baire space Forcing Axioms Ramsey theory over partitions Microscopic Approach OCA Sigma-Prikry Diamond for trees Slim tree Singular cardinals combinatorics Erdos-Hajnal graphs Open Access Uniformization reflection principles Whitehead Problem 54G20 stationary hitting Ineffable cardinal Was Ulam right HOD ccc Poset positive partition relation Almost countably chromatic square nonmeager set Amenable C-sequence strongly bounded groups Almost-disjoint family Club Guessing Diamond-sharp diamond star Strong coloring Reduced Power P-Ideal Dichotomy stick Vanishing levels Commutative cancellative semigroups Knaster and friends Cardinal function Erdos Cardinal SNR Strongly Luzin set Martin's Axiom specializable Souslin tree Filter reflection Foundations Prikry-type forcing Antichain Subtle tree property Kurepa Hypothesis S-Space transformations countably metacompact PFA(S)[S] Postprocessing function Sakurai's Bell inequality GMA tensor product graph Dushnik-Miller Hedetniemi's conjecture Ostaszewski square Chang's conjecture Selective Ultrafilter PFA Fodor-type reflection free Boolean algebra full tree b-scale middle diamond Coherent tree Successor of Regular Cardinal Forcing club_AD indecomposable ultrafilter Uniformly homogeneous L-space Singular cofinality Cardinal Invariants approachability ideal Precaliber Shelah's Strong Hypothesis Luzin set
Tag Archives: 03E05
Fake Reflection
Joint work with Gabriel Fernandes and Miguel Moreno. Abstract. We introduce a generalization of stationary set reflection which we call filter reflection, and show it is compatible with the axiom of constructibility as well as with strong forcing axioms. We … Continue reading
Knaster and friends II: The C-sequence number
Joint work with Chris Lambie-Hanson. Abstract. Motivated by a characterization of weakly compact cardinals due to Todorcevic, we introduce a new cardinal characteristic, the C-sequence number, which can be seen as a measure of the compactness of a regular uncountable … Continue reading
A remark on Schimmerling’s question
Joint work with Ari Meir Brodsky. Abstract. Schimmerling asked whether $\square^*_\lambda$ together with GCH entails the existence of a $\lambda^+$-Souslin tree, for a singular cardinal $\lambda$. Here, we provide an affirmative answer under the additional assumption that there exists a … Continue reading
Weak square and stationary reflection
Joint work with Gunter Fuchs. Abstract. It is well-known that the square principle $\square_\lambda$ entails the existence of a non-reflecting stationary subset of $\lambda^+$, whereas the weak square principle $\square^*_\lambda$ does not. Here we show that if $\mu^{cf(\lambda)}<\lambda$ for all $\mu<\lambda$, … Continue reading
Posted in Publications, Squares and Diamonds
Tagged 03E05, 03E35, 03E57, Diamond, Forcing Axioms, stationary reflection, weak square
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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 $\lambda$, … Continue reading
Posted in Publications, Souslin Hypothesis
Tagged 03E05, 03E35, 03E57, Diamond, Forcing Axioms, Souslin Tree, square, super-Souslin tree
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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
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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
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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, square, xbox
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Reduced powers of Souslin trees
Joint work with Ari Meir Brodsky. Abstract. We study the relationship between a $\kappa$-Souslin tree $T$ and its reduced powers $T^\theta/\mathcal U$. Previous works addressed this problem from the viewpoint of a single power $\theta$, whereas here, tools are developed … Continue reading