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