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stationary reflection Knaster and friends weak Kurepa tree Minimal Walks Commutative cancellative semigroups club_AD Rock n' Roll diamond star specializable Souslin tree Well-behaved magma Ineffable cardinal Constructible Universe incompactness Sigma-Prikry Ascent Path Almost Souslin Nonspecial tree Cardinal Invariants indecomposable ultrafilter Subnormal ideal polarized partition relation stick Forcing Axioms Shelah's Strong Hypothesis Almost countably chromatic Uniformly homogeneous Absoluteness Fat stationary set super-Souslin tree 54G20 nonmeager set ZFC construction coloring number Universal Sequences Coherent tree Mandelbrot set Strongly Luzin set Distributive tree Dowker space Poset Axiom R positive partition relation Chang's conjecture higher Baire space O-space unbounded function Knaster Erdos Cardinal Successor of Regular Cardinal Local Club Condensation. AIM forcing Martin's Axiom GMA weak square Hindman's Theorem Foundations Uniformly coherent Large Cardinals Lipschitz reduction Ramsey theory over partitions Microscopic Approach PFA(S)[S] Kurepa Hypothesis Greatly Mahlo PFA Diamond Vanishing levels Diamond-sharp Precaliber Parameterized proxy principle SNR Dushnik-Miller Prikry-type forcing L-space Reflecting stationary set strongly bounded groups S-Space free Boolean algebra Hereditarily Lindelöf space Forcing Closed coloring Cardinal function Uniformization Fast club Fodor-type reflection Square-Brackets Partition Relations square principles Antichain projective Boolean algebra very good scale Chromatic number Subadditive Sierpinski's onto mapping principle Partition Relations middle diamond Singular cofinality free Souslin tree xbox full tree Small forcing Singular Density Selective Ultrafilter Was Ulam right Aronszajn tree Filter reflection Reduced Power Ulam matrix approachability ideal regressive Souslin tree Non-saturation reflection principles Postprocessing function Sakurai's Bell inequality Open Access weak diamond Iterated forcing square Generalized descriptive set theory tensor product graph Erdos-Hajnal graphs Jonsson cardinal Cohen real Whitehead Problem Luzin set Club Guessing Strong coloring Successor of Singular Cardinal Diamond for trees Singular cardinals combinatorics transformations Rainbow sets Amenable C-sequence C-sequence HOD Subtle tree property Ostaszewski square Weakly compact cardinal Rado's conjecture Analytic sets Hedetniemi's conjecture Subtle cardinal ccc Almost-disjoint family sap P-Ideal Dichotomy countably metacompact OCA stationary hitting Prevalent singular cardinals Generalized Clubs b-scale Souslin Tree Slim tree
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