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