Archives
Keywords
Uniformly homogeneous Weakly compact cardinal Hereditarily Lindelöf space Mandelbrot set P-Ideal Dichotomy Strong coloring approachability ideal Subtle tree property super-Souslin tree Almost Souslin Luzin set Coherent tree Non-saturation Prevalent singular cardinals Whitehead Problem weak Kurepa tree Slim tree Singular cofinality Fat stationary set Antichain Strongly Luzin set Cardinal Invariants projective Boolean algebra Small forcing Uniformly coherent specializable Souslin tree Ineffable cardinal Aronszajn tree Vanishing levels Prikry-type forcing Knaster and friends Fast club Sigma-Prikry strongly bounded groups Subnormal ideal Rock n' Roll Well-behaved magma Sierpinski's onto mapping principle Souslin Tree HOD Erdos Cardinal Lipschitz reduction Nonspecial tree Dushnik-Miller weak square incompactness transformations Axiom R Jonsson cardinal Generalized descriptive set theory O-space tensor product graph Hindman's Theorem Chang's conjecture reflection principles Greatly Mahlo Club Guessing free Boolean algebra stationary reflection Forcing Axioms Amenable C-sequence PFA(S)[S] Generalized Clubs Successor of Regular Cardinal Diamond for trees coloring number Erdos-Hajnal graphs Almost countably chromatic unbounded function Forcing Ulam matrix weak diamond regressive Souslin tree Almost-disjoint family sap Uniformization ccc Minimal Walks 54G20 polarized partition relation Poset Foundations Large Cardinals b-scale Filter reflection Selective Ultrafilter Singular Density middle diamond square principles club_AD Shelah's Strong Hypothesis S-Space Knaster Local Club Condensation. AIM forcing Subtle cardinal Hedetniemi's conjecture Microscopic Approach Chromatic number Martin's Axiom GMA Rainbow sets Diamond Closed coloring Ostaszewski square diamond star xbox Precaliber Distributive tree Diamond-sharp square Kurepa Hypothesis L-space Reflecting stationary set positive partition relation full tree Square-Brackets Partition Relations free Souslin tree stick Rado's conjecture Cardinal function Reduced Power higher Baire space Postprocessing function Cohen real Sakurai's Bell inequality OCA Ascent Path Singular cardinals combinatorics Fodor-type reflection PFA Partition Relations Universal Sequences Analytic sets Parameterized proxy principle indecomposable ultrafilter Constructible Universe nonmeager set C-sequence Subadditive Successor of Singular Cardinal Dowker space Ramsey theory over partitions stationary hitting ZFC construction Iterated forcing very good scale Absoluteness Commutative cancellative semigroups countably metacompact Open Access SNR Was Ulam right
Tag Archives: 03E04
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
On topological spaces of singular density and minimal weight
Abstract: We introduce a weakening of the Generalized Continuum Hypothesis, which we will refer to as the Prevalent Singular cardinals Hypothesis (PSH), and show it implies that every topological space of density and weight $\aleph_{\omega_1}$ is not hereditarily Lindelöf. The assumption … Continue reading
A topological reflection principle equivalent to Shelah’s strong hypothesis
Abstract: We notice that Shelah’s Strong Hypothesis (SSH) is equivalent to the following reflection principle: Suppose $\mathbb X$ is an (infinite) first-countable space whose density is a regular cardinal, $\kappa$. If every separable subspace of $\mathbb X$ is of cardinality at most … Continue reading
Posted in Compactness, Publications, Topology
Tagged 03E04, 03E65, 54G15, Open Access, Shelah's Strong Hypothesis
Leave a comment
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
On the consistency strength of the Milner-Sauer conjecture
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 conjecture is consistent and known … 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
