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