Archives
Keywords
Ascent Path Interval topology on trees Sigma-Prikry Diamond-sharp Sierpinski's onto mapping principle countably metacompact Subtle cardinal Prevalent singular cardinals Greatly Mahlo Open Access Forcing Axioms Subtle tree property Filter reflection Prikry-type forcing Knaster Whitehead Problem perfectly normal reflection principles Singular Density free Souslin tree Hindman's Theorem Chromatic number Microscopic Approach Was Ulam right? Dowker space Fast club full tree Hedetniemi's conjecture Generalized descriptive set theory nonmeager set Luzin set Rock n' Roll Uniformization very good scale Cardinal function Vanishing levels indecomposable filter Small forcing Almost Souslin Respecting tree weak square Cardinal Invariants Hereditarily Lindelöf space Parameterized proxy principle middle diamond Coherent tree Poset Local Club Condensation. Reduced Power Successor of Singular Cardinal weak Kurepa tree Club Guessing transformations Fodor-type reflection L-space b-scale 54G20 coloring number square principles Cohen real Antichain Kurepa Hypothesis P-Ideal Dichotomy AIM forcing Universal Sequences Singular cofinality super-Souslin tree club_AD Axiom R tensor product graph sap Subadditive PFA approachability ideal Ascending path weak diamond Countryman line Erdos Cardinal Forcing with side conditions Intersection model ZFC construction Diamond projective Boolean algebra Ulam matrix Weakly compact cardinal Knaster and friends specializable Souslin tree Singular cardinals combinatorics higher Baire space Partition relations for trees regressive Souslin tree Postprocessing function Minimal Walks Strongly compact cardinal Successor of Regular Cardinal Ostaszewski square Iterated forcing Reflecting stationary set Square-Brackets Partition Relations Analytic sets Rainbow sets Aronszajn tree ccc Slim tree Large Cardinals Diamond for trees OCA Distributive tree positive partition relation Partition Relations HOD Foundations Sakurai's Bell inequality Strongly Luzin set Ramsey theory over partitions Shelah's Strong Hypothesis Amenable C-sequence Entangled linear order Non-saturation Precaliber Selective Ultrafilter PFA(S)[S] Closed coloring Strong coloring diamond star free Boolean algebra stationary hitting SNR Absoluteness Commutative cancellative semigroups Commutative projection system Jonsson cardinal Chang's conjecture Nonspecial tree Rado's conjecture Souslin Tree Uniformly homogeneous Ineffable cardinal Erdos-Hajnal graphs Lipschitz reduction S-Space Monotonically far O-space Martin's Axiom GMA Uniformly coherent Subnormal ideal stationary reflection Dushnik-Miller Almost-disjoint family xbox C-sequence Forcing strongly bounded groups Almost countably chromatic Fat stationary set incompactness Constructible Universe Mandelbrot set polarized partition relation Well-behaved magma unbounded function Generalized Clubs stick square
Tag Archives: sap
Knaster and friends III: Subadditive colorings
Joint work with Chris Lambie-Hanson. Abstract. We continue our study of strongly unbounded colorings, this time focusing on subadditive maps. In Part I of this series, we showed that, for many pairs of infinite cardinals $\theta < \kappa$, the existence … Continue reading
Jensen’s diamond principle and its relatives
This is chapter 6 in the book Set Theory and Its Applications (ISBN: 0821848127). Abstract: We survey some recent results on the validity of Jensen’s diamond principle at successor cardinals. We also discuss weakening of this principle such as club … 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
A relative of the approachability ideal, diamond and non-saturation
Abstract: Let $\lambda$ denote a singular cardinal. Zeman, improving a previous result of Shelah, proved that $\square^*_\lambda$ together with $2^\lambda=\lambda^+$ implies $\diamondsuit_S$ for every $S\subseteq\lambda^+$ that reflects stationarily often. In this paper, for a subset $S\subset\lambda^+$, a normal subideal of … Continue reading
