Archives
Keywords
Ascending path super-Souslin tree Ostaszewski square Ineffable cardinal Uniformly homogeneous Forcing with side conditions Singular Density Almost countably chromatic full tree L-space strongly bounded groups Subadditive Reflecting stationary set Chang's conjecture Minimal Walks Commutative cancellative semigroups Weakly compact cardinal weak Kurepa tree Universal Sequences Closed coloring square Precaliber higher Baire space Analytic sets Local Club Condensation. Reduced Power PFA(S)[S] Distributive tree Subtle cardinal O-space Uniformly coherent specializable Souslin tree Rado's conjecture Open Access GMA Ulam matrix Well-behaved magma Filter reflection Sierpinski's onto mapping principle free Souslin tree Fat stationary set Absoluteness Singular cardinals combinatorics Uniformization S-Space Postprocessing function Large Cardinals Poset Hindman's Theorem Subtle tree property incompactness Luzin set PFA ccc Prevalent singular cardinals nonmeager set Sigma-Prikry Whitehead Problem indecomposable filter square principles Cardinal function Ramsey theory over partitions approachability ideal sap Forcing Axioms transformations Forcing Kurepa Hypothesis Greatly Mahlo Fodor-type reflection Diamond-sharp Successor of Singular Cardinal Axiom R ZFC construction middle diamond Strongly compact cardinal Constructible Universe coloring number Subnormal ideal Cardinal Invariants projective Boolean algebra Partition relations for trees Intersection model Almost-disjoint family very good scale Almost Souslin positive partition relation perfectly normal Generalized Clubs OCA Souslin Tree Nonspecial tree stick Interval topology on trees Microscopic Approach diamond star Vanishing levels Amenable C-sequence tensor product graph AIM forcing stationary reflection Countryman line Jonsson cardinal Singular cofinality 54G20 Erdos-Hajnal graphs regressive Souslin tree b-scale weak diamond Slim tree Hedetniemi's conjecture stationary hitting Cohen real Lipschitz reduction Sakurai's Bell inequality xbox Foundations Was Ulam right? Diamond for trees Commutative projection system Strong coloring Entangled linear order Strongly Luzin set unbounded function Square-Brackets Partition Relations Knaster and friends Selective Ultrafilter HOD polarized partition relation C-sequence Club Guessing Fast club Successor of Regular Cardinal Respecting tree SNR Ascent Path Iterated forcing Martin's Axiom Hereditarily Lindelöf space Rainbow sets Rock n' Roll Dowker space Aronszajn tree Knaster P-Ideal Dichotomy Chromatic number Erdos Cardinal Diamond countably metacompact Generalized descriptive set theory Coherent tree Partition Relations weak square Parameterized proxy principle Monotonically far club_AD Shelah's Strong Hypothesis reflection principles Non-saturation Prikry-type forcing Antichain Small forcing free Boolean algebra Baumgartner's square Mandelbrot set Dushnik-Miller
Tag Archives: 03E35
A cofinality-preserving small forcing may introduce a special Aronszajn tree
Extended Abstract: Shelah proved that Cohen forcing introduces a Souslin tree; Jensen proved that a c.c.c. forcing may consistently add a Kurepa tree; Todorcevic proved that a Knaster poset may already force the Kurepa hypothesis; Irrgang introduced a c.c.c. notion … Continue reading
Posted in Publications, Squares and Diamonds
Tagged 03E04, 03E05, 03E35, Aronszajn tree, Small forcing, Successor of Singular Cardinal, weak square
Leave a comment
Openly generated Boolean algebras and the Fodor-type reflection principle
Joint work with Sakaé Fuchino. Abstract: We prove that the Fodor-type Reflection Principle (FRP) is equivalent to the assertion that any Boolean algebra is openly generated if and only if it is $\aleph _2$-projective. Previously it was known that this … Continue reading
Posted in Compactness, Publications
Tagged 03E35, 03E55, 03E65, 03E75, 03G05, 06E05, Axiom R, Fodor-type reflection, free Boolean algebra, projective Boolean algebra, Shelah's Strong Hypothesis, stationary reflection
Comments Off on Openly generated Boolean algebras and the Fodor-type reflection principle
The failure of diamond on a reflecting stationary set
Joint work with Moti Gitik. Abstract: It is shown that the failure of $\diamondsuit_S$, for a subset $S\subseteq\aleph_{\omega+1}$ that reflects stationarily often, is consistent with GCH and $\text{AP}_{\aleph_\omega}$, relatively to the existence of a supercompact cardinal. This should be comapred with … Continue reading
A relative of the approachability ideal, diamond and non-saturation
Abstract: Let $\lambda$ denote a singular cardinal. Zeman, improving a previous result of Shelah, proved that $\square^*_\lambda$ together with $2^\lambda=\lambda^+$ implies $\diamondsuit_S$ for every $S\subseteq\lambda^+$ that reflects stationarily often. In this paper, for a subset $S\subset\lambda^+$, a normal subideal of … Continue reading
On guessing generalized clubs at the successors of regulars
Abstract: Konig, Larson and Yoshinobu initiated the study of principles for guessing generalized clubs, and introduced a construction of an higher Souslin tree from the strong guessing principle. Complementary to the author’s work on the validity of diamond and non-saturation … Continue reading
Antichains in partially ordered sets of singular cofinality
Abstract: In their paper from 1981, Milner and Sauer conjectured that for any poset $\mathbb P$, if $\text{cf}(\mathbb P)$ is a singular cardinal $\lambda$, then $\mathbb P$ must contain an antichain of size $\text{cf}(\lambda)$. The main result of of this … Continue reading
Posted in Publications, Singular Cardinals Combinatorics
Tagged 03E04, 03E35, 06A07, Antichain, Poset, Singular cofinality
Leave a comment
The Ostaszewski square, and homogeneous Souslin trees
Abstract: Assume GCH and let $\lambda$ denote an uncountable cardinal. We prove that if $\square_\lambda$ holds, then this may be witnessed by a coherent sequence $\left\langle C_\alpha \mid \alpha<\lambda^+\right\rangle$ with the following remarkable guessing property: For every sequence $\langle A_i\mid i<\lambda\rangle$ … Continue reading
Posted in Publications, Souslin Hypothesis, Squares and Diamonds
Tagged 03E05, 03E35, Club Guessing, Fat stationary set, Ostaszewski square, Souslin Tree
5 Comments
