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