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