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S-Space regressive Souslin tree Reduced Power Cohen real b-scale square Diamond for trees Rado's conjecture Weakly compact cardinal Almost countably chromatic Coherent tree Subtle cardinal Fodor-type reflection Minimal Walks very good scale club_AD Aronszajn tree free Souslin tree Nonspecial tree Precaliber AIM forcing Dowker space Large Cardinals weak square Well-behaved magma positive partition relation Reflecting stationary set Microscopic Approach Luzin set Diamond strongly bounded groups Kurepa Hypothesis xbox polarized partition relation Small forcing Erdos Cardinal Sakurai's Bell inequality Parameterized proxy principle nonmeager set GMA Closed coloring Cardinal function Open Access Erdos-Hajnal graphs HOD super-Souslin tree Greatly Mahlo SNR countably metacompact approachability ideal PFA Foundations Chang's conjecture Sierpinski's onto mapping principle Absoluteness Rainbow sets stationary reflection Diamond-sharp Uniformly homogeneous stationary hitting Almost-disjoint family Knaster and friends ZFC construction Sigma-Prikry square principles Prevalent singular cardinals Iterated forcing Prikry-type forcing Axiom R 54G20 Cardinal Invariants indecomposable ultrafilter Generalized Clubs Ostaszewski square Fast club stick full tree Martin's Axiom Amenable C-sequence Knaster Hindman's Theorem Dushnik-Miller Whitehead Problem Mandelbrot set sap Ulam matrix incompactness Successor of Singular Cardinal Hereditarily Lindelöf space Subadditive Partition Relations weak Kurepa tree Non-saturation Successor of Regular Cardinal Ramsey theory over partitions Singular Density C-sequence Antichain Shelah's Strong Hypothesis O-space Jonsson cardinal reflection principles Chromatic number Selective Ultrafilter Rock n' Roll Strong coloring coloring number Constructible Universe projective Boolean algebra Subnormal ideal Filter reflection Slim tree Uniformization weak diamond Forcing Axioms Local Club Condensation. Singular cardinals combinatorics Fat stationary set Vanishing levels Hedetniemi's conjecture Poset Postprocessing function L-space Forcing Was Ulam right PFA(S)[S] specializable Souslin tree tensor product graph Analytic sets diamond star Almost Souslin Ascent Path transformations Club Guessing higher Baire space Singular cofinality Subtle tree property ccc free Boolean algebra Generalized descriptive set theory unbounded function Strongly Luzin set Universal Sequences OCA Ineffable cardinal Distributive tree Souslin Tree Lipschitz reduction middle diamond Square-Brackets Partition Relations Commutative cancellative semigroups Uniformly coherent P-Ideal Dichotomy
Tag Archives: Open Access
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 guessing generalized clubs at the successors of regulars
Abstract: Konig, Larson and Yoshinobu initiated the study of principles for guessing generalized clubs, and introduced a construction of an higher Souslin tree from the strong guessing principle. Complementary to the author’s work on the validity of diamond and non-saturation … 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
Transforming rectangles into squares, with applications to strong colorings
Abstract: It is proved that every singular cardinal $\lambda$ admits a function $\textbf{rts}:[\lambda^+]^2\rightarrow[\lambda^+]^2$ that transforms rectangles into squares. That is, whenever $A,B$ are cofinal subsets of $\lambda^+$, we have $\textbf{rts}[A\circledast B]\supseteq C\circledast C$, for some cofinal subset $C\subseteq\lambda^+$. As a … Continue reading
