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