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