Archives
Keywords
OCA very good scale stationary hitting club_AD strongly bounded groups Uniformization Axiom R tensor product graph HOD Analytic sets Microscopic Approach Mandelbrot set Absoluteness Fast club Jonsson cardinal indecomposable filter middle diamond Forcing Axioms Sigma-Prikry Fodor-type reflection Uniformly coherent Hindman's Theorem Local Club Condensation. Closed coloring Iterated forcing Singular cardinals combinatorics Erdos Cardinal Countryman line Whitehead Problem countably metacompact Cardinal function Club Guessing Precaliber Large Cardinals Almost-disjoint family Distributive tree Sierpinski's onto mapping principle Diamond for trees Shelah's Strong Hypothesis diamond star Chang's conjecture Singular cofinality Knaster ZFC construction Slim tree super-Souslin tree Nonspecial tree Entangled linear order Generalized Clubs Postprocessing function Commutative projection system Luzin set square Coherent tree Antichain Amenable C-sequence Chromatic number Selective Ultrafilter Well-behaved magma Subtle cardinal 54G20 Knaster and friends Hereditarily Lindelöf space Reflecting stationary set SNR Interval topology on trees GMA Respecting tree Partition Relations Diamond-sharp unbounded function S-Space PFA Open Access Constructible Universe Subtle tree property Universal Sequences Ramsey theory over partitions Cohen real stationary reflection positive partition relation Diamond Reduced Power higher Baire space Generalized descriptive set theory Lipschitz reduction Prevalent singular cardinals weak square Minimal Walks Singular Density Strongly Luzin set Intersection model square principles Forcing Vanishing levels Subadditive free Boolean algebra Foundations Cardinal Invariants Dowker space specializable Souslin tree free Souslin tree Successor of Singular Cardinal Ostaszewski square Ascent Path incompactness Hedetniemi's conjecture Almost Souslin Strongly compact cardinal Martin's Axiom Poset Uniformly homogeneous projective Boolean algebra Kurepa Hypothesis C-sequence b-scale Commutative cancellative semigroups reflection principles Non-saturation Weakly compact cardinal sap Small forcing Dushnik-Miller Parameterized proxy principle AIM forcing Forcing with side conditions Ascending path Partition relations for trees perfectly normal Souslin Tree Almost countably chromatic Greatly Mahlo approachability ideal Ulam matrix L-space PFA(S)[S] Fat stationary set Ineffable cardinal P-Ideal Dichotomy Subnormal ideal transformations Square-Brackets Partition Relations nonmeager set Erdos-Hajnal graphs O-space Rado's conjecture Prikry-type forcing full tree xbox Strong coloring polarized partition relation weak Kurepa tree weak diamond Rainbow sets Aronszajn tree Sakurai's Bell inequality ccc Successor of Regular Cardinal Filter reflection regressive Souslin tree coloring number stick Monotonically far Rock n' Roll Was Ulam right?
Tag Archives: Shelah’s Strong Hypothesis
Logic in Hungary, August 2005
These are the slides of a contributed talk given at the Logic in Hungary 2005 meeting (Budapest, 5–11 August 2005). Talk Title: On the consistency strength of the Milner-Sauer Conjecture Abstract: In their paper from 1981, after learning about Pouzet‘s theorem that any … Continue reading
Posted in Contributed Talks
Tagged Antichain, Shelah's Strong Hypothesis, Singular cofinality
Leave a comment
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
Comments Off on A topological reflection principle equivalent to Shelah’s strong hypothesis
Openly generated Boolean algebras and the Fodor-type reflection principle
Joint work with Sakaé Fuchino. Abstract: We prove that the Fodor-type Reflection Principle (FRP) is equivalent to the assertion that any Boolean algebra is openly generated if and only if it is $\aleph _2$-projective. Previously it was known that this … Continue reading
Posted in Compactness, Publications
Tagged 03E35, 03E55, 03E65, 03E75, 03G05, 06E05, Axiom R, Fodor-type reflection, free Boolean algebra, projective Boolean algebra, Shelah's Strong Hypothesis, stationary reflection
Comments Off on Openly generated Boolean algebras and the Fodor-type reflection principle
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
