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Reflecting stationary set Chang's conjecture approachability ideal Forcing Hereditarily Lindelöf space Coherent tree stationary reflection reflection principles Microscopic Approach Sakurai's Bell inequality PFA Subadditive Successor of Singular Cardinal Singular Density C-sequence Strongly compact cardinal regressive Souslin tree stationary hitting PFA(S)[S] countably metacompact HOD Distributive tree Axiom R Knaster and friends Prevalent singular cardinals Local Club Condensation. AIM forcing SNR ccc Ulam matrix higher Baire space middle diamond Whitehead Problem Precaliber Poset Countryman line Closed coloring Slim tree incompactness Absoluteness Strongly Luzin set Luzin set Cardinal function Fast club Subtle cardinal Erdos Cardinal Almost countably chromatic weak square Well-behaved magma Generalized Clubs P-Ideal Dichotomy S-Space Foundations Universal Sequences Erdos-Hajnal graphs Almost-disjoint family Almost Souslin square Diamond for trees Constructible Universe Mandelbrot set Subnormal ideal coloring number Successor of Regular Cardinal Ramsey theory over partitions Square-Brackets Partition Relations Commutative projection system Lipschitz reduction Uniformly coherent Subtle tree property Commutative cancellative semigroups Interval topology on trees Hedetniemi's conjecture Vanishing levels Nonspecial tree Forcing with side conditions Small forcing Aronszajn tree Jonsson cardinal Analytic sets square principles diamond star Entangled linear order Martin's Axiom Dushnik-Miller Sierpinski's onto mapping principle Cardinal Invariants Cohen real xbox Antichain Hindman's Theorem Knaster tensor product graph indecomposable filter unbounded function very good scale Intersection model Ascent Path Strong coloring Singular cofinality Iterated forcing Rock n' Roll Kurepa Hypothesis Reduced Power Ostaszewski square Non-saturation 54G20 Dowker space Uniformization club_AD full tree Selective Ultrafilter strongly bounded groups positive partition relation Club Guessing free Souslin tree Greatly Mahlo Souslin Tree super-Souslin tree Uniformly homogeneous Forcing Axioms weak Kurepa tree Partition Relations Minimal Walks perfectly normal Sigma-Prikry Was Ulam right? Diamond-sharp Amenable C-sequence transformations L-space Fodor-type reflection Filter reflection Generalized descriptive set theory Chromatic number Rainbow sets GMA Ascending path Monotonically far Respecting tree Large Cardinals Parameterized proxy principle sap projective Boolean algebra Ineffable cardinal Postprocessing function Weakly compact cardinal polarized partition relation Prikry-type forcing Rado's conjecture specializable Souslin tree stick free Boolean algebra Fat stationary set nonmeager set Singular cardinals combinatorics ZFC construction Shelah's Strong Hypothesis Open Access O-space b-scale Diamond weak diamond OCA
Tag Archives: 03E05
Ketonen’s question and other cardinal sins
Joint work with Zhixing You and Jiachen Yuan. Abstract. Answering a question of Ketonen from the late 1970’s, it is proved that a weakly compact cardinal carrying an indecomposable ultrafilter need not be measurable. The result is obtained by analyzing … Continue reading
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, Respecting tree, square, xbox
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