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