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