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