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