Archives
Keywords
Iterated forcing PFA(S)[S] Ascent Path Dushnik-Miller Ineffable cardinal HOD Ostaszewski square Prikry-type forcing Well-behaved magma S-Space Ramsey theory over partitions Partition Relations Martin's Axiom Forcing Knaster and friends super-Souslin tree Subnormal ideal Amenable C-sequence stationary reflection SNR Strongly Luzin set Whitehead Problem middle diamond Sigma-Prikry b-scale 54G20 incompactness Nonspecial tree Shelah's Strong Hypothesis strongly bounded groups Uniformly homogeneous free Boolean algebra Aronszajn tree ccc ZFC construction Hedetniemi's conjecture Singular Density Strong coloring C-sequence Slim tree Diamond-sharp free Souslin tree club_AD Antichain full tree transformations Closed coloring Poset reflection principles xbox Constructible Universe Rainbow sets Generalized descriptive set theory Selective Ultrafilter Square-Brackets Partition Relations Open Access very good scale Successor of Singular Cardinal Club Guessing Erdos-Hajnal graphs Weakly compact cardinal positive partition relation diamond star Vanishing levels Forcing Axioms Rado's conjecture L-space weak diamond Dowker space Chromatic number Cardinal function Chang's conjecture OCA AIM forcing Rock n' Roll regressive Souslin tree Subtle cardinal Uniformly coherent Small forcing Singular cardinals combinatorics Almost-disjoint family Cardinal Invariants Subadditive Fodor-type reflection Singular cofinality Foundations Fast club Was Ulam right Successor of Regular Cardinal Microscopic Approach Prevalent singular cardinals Parameterized proxy principle Kurepa Hypothesis Coherent tree Filter reflection stick PFA Erdos Cardinal Lipschitz reduction Diamond for trees Reduced Power approachability ideal Minimal Walks Universal Sequences Souslin Tree Almost countably chromatic Cohen real Jonsson cardinal square Almost Souslin Greatly Mahlo nonmeager set Generalized Clubs Fat stationary set Analytic sets square principles Luzin set Knaster specializable Souslin tree Axiom R projective Boolean algebra O-space coloring number indecomposable ultrafilter stationary hitting P-Ideal Dichotomy Mandelbrot set Hereditarily Lindelöf space Uniformization weak square Distributive tree Sierpinski's onto mapping principle Absoluteness Non-saturation Sakurai's Bell inequality Postprocessing function weak Kurepa tree Precaliber GMA countably metacompact Ulam matrix Large Cardinals Local Club Condensation. Subtle tree property higher Baire space Hindman's Theorem Commutative cancellative semigroups polarized partition relation sap tensor product graph Diamond Reflecting stationary set unbounded function
Tag Archives: 05C05
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
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
Reduced powers of Souslin trees
Joint work with Ari Meir Brodsky. Abstract. We study the relationship between a $\kappa$-Souslin tree $T$ and its reduced powers $T^\theta/\mathcal U$. Previous works addressed this problem from the viewpoint of a single power $\theta$, whereas here, tools are developed … Continue reading
