Archives
Keywords
Analytic sets Vanishing levels club_AD Axiom R strongly bounded groups Sigma-Prikry Subtle cardinal weak square Club Guessing weak diamond Greatly Mahlo Strongly compact cardinal tensor product graph Large Cardinals countably metacompact coloring number approachability ideal indecomposable ultrafilter Absoluteness Slim tree Luzin set square Almost-disjoint family Subtle tree property Chromatic number Diamond Commutative cancellative semigroups Singular cardinals combinatorics Postprocessing function free Souslin tree specializable Souslin tree Fast club Forcing diamond star transformations very good scale super-Souslin tree unbounded function Rock n' Roll ccc Non-saturation P-Ideal Dichotomy Diamond for trees Nonspecial tree Parameterized proxy principle Generalized Clubs Minimal Walks Sierpinski's onto mapping principle Diamond-sharp Cardinal Invariants Mandelbrot set Almost countably chromatic Filter reflection Dushnik-Miller Universal Sequences Generalized descriptive set theory Rado's conjecture Ascent Path Dowker space stationary reflection Strong coloring weak Kurepa tree Kurepa Hypothesis polarized partition relation Uniformly homogeneous Antichain SNR Martin's Axiom middle diamond incompactness Hindman's Theorem Singular cofinality higher Baire space Precaliber Reflecting stationary set reflection principles Foundations stationary hitting Reduced Power Aronszajn tree Ramsey theory over partitions nonmeager set Cohen real Open Access Closed coloring Prikry-type forcing free Boolean algebra Partition Relations Distributive tree Whitehead Problem Microscopic Approach b-scale HOD square principles Poset Subnormal ideal Coherent tree Almost Souslin Sakurai's Bell inequality Iterated forcing Erdos-Hajnal graphs Rainbow sets Selective Ultrafilter Hedetniemi's conjecture OCA Jonsson cardinal Uniformization Ostaszewski square Square-Brackets Partition Relations PFA(S)[S] GMA Was Ulam right? sap Ulam matrix O-space Chang's conjecture Hereditarily Lindelöf space Knaster Subadditive Well-behaved magma S-Space Fodor-type reflection Amenable C-sequence Weakly compact cardinal Ineffable cardinal xbox Successor of Singular Cardinal regressive Souslin tree Souslin Tree AIM forcing PFA 54G20 Prevalent singular cardinals Strongly Luzin set L-space positive partition relation Local Club Condensation. Erdos Cardinal Successor of Regular Cardinal Knaster and friends Cardinal function stick Uniformly coherent ZFC construction Fat stationary set Lipschitz reduction Intersection model Constructible Universe Respecting tree Forcing Axioms Small forcing full tree projective Boolean algebra Singular Density Commutative projection system C-sequence Shelah's Strong Hypothesis Countryman line
Tag Archives: 03E05
Ketonen’s question and other cardinal sins
Joint work with Zhixing You and Jiachen Yuan. Abstract. Intersection models of generic extensions obtained from a commutative projection systems of notions of forcing has recently regained interest, especially in the study of descriptive set theory. Here, we show that … Continue reading
Posted in Compactness, Preprints
Tagged 03E05, 03E35, 03E55, Ascent Path, C-sequence, Commutative projection system, indecomposable ultrafilter, Intersection model, Strongly compact cardinal
Comments Off on Ketonen’s question and other cardinal sins
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
Weak square and stationary reflection
Joint work with Gunter Fuchs. Abstract. It is well-known that the square principle
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
Posted in Publications, Souslin Hypothesis
Tagged 03E05, 03E35, 03E57, 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
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
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
Posted in Publications, Squares and Diamonds
Tagged 03E05, 03E45, Almost Souslin, diamond star, Kurepa Hypothesis, Minimal Walks, Respecting tree, square, xbox
1 Comment
