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