Archives
Keywords
full tree Vanishing levels SNR Poset Martin's Axiom Absoluteness O-space Diamond-sharp Successor of Singular Cardinal HOD Uniformization super-Souslin tree Successor of Regular Cardinal Subtle cardinal Diamond Weakly compact cardinal Small forcing Universal Sequences Selective Ultrafilter approachability ideal Coherent tree stationary reflection club_AD Dushnik-Miller Subnormal ideal Rock n' Roll Was Ulam right Greatly Mahlo Hedetniemi's conjecture Kurepa Hypothesis Diamond for trees Singular Density Rainbow sets Filter reflection Sigma-Prikry Chang's conjecture Cardinal Invariants Partition Relations very good scale Rado's conjecture Forcing transformations Knaster Fodor-type reflection Precaliber diamond star Mandelbrot set Axiom R tensor product graph Local Club Condensation. Souslin Tree C-sequence Analytic sets Almost-disjoint family S-Space Shelah's Strong Hypothesis nonmeager set Hereditarily Lindelöf space Uniformly homogeneous Lipschitz reduction Uniformly coherent reflection principles stick Luzin set Forcing Axioms Ramsey theory over partitions 54G20 free Souslin tree Singular cofinality stationary hitting Jonsson cardinal Distributive tree sap weak square incompactness Parameterized proxy principle square Aronszajn tree polarized partition relation regressive Souslin tree b-scale Reduced Power Open Access Generalized descriptive set theory projective Boolean algebra Almost Souslin unbounded function countably metacompact P-Ideal Dichotomy Subadditive Amenable C-sequence Strong coloring OCA Club Guessing Generalized Clubs specializable Souslin tree indecomposable ultrafilter Sierpinski's onto mapping principle L-space Large Cardinals strongly bounded groups Fat stationary set Chromatic number Antichain Foundations Ascent Path Constructible Universe Ineffable cardinal Cardinal function Ostaszewski square Reflecting stationary set middle diamond xbox Strongly Luzin set Fast club Closed coloring Postprocessing function Commutative cancellative semigroups PFA Knaster and friends Singular cardinals combinatorics Microscopic Approach Iterated forcing Square-Brackets Partition Relations Subtle tree property coloring number positive partition relation GMA Whitehead Problem Well-behaved magma Erdos Cardinal weak diamond Erdos-Hajnal graphs Dowker space Cohen real higher Baire space Almost countably chromatic AIM forcing square principles Slim tree Sakurai's Bell inequality Prevalent singular cardinals free Boolean algebra ZFC construction Nonspecial tree Ulam matrix ccc Hindman's Theorem PFA(S)[S] Minimal Walks Prikry-type forcing Non-saturation
Tag Archives: Forcing Axioms
Squares, ultrafilters and forcing axioms
Joint work with Chris Lambie-Hanson and Jing Zhang. Abstract. We study the interplay of the three families of combinatorial objects or principles. Specifically, we show the following. Strong forcing axioms, in general incompatible with the existence of indexed squares, can … Continue reading
Posted in Compactness, Preprints
Tagged Forcing Axioms, indecomposable ultrafilter, Subadditive, unbounded function
Comments Off on Squares, ultrafilters and forcing axioms
Weak square and stationary reflection
Joint work with Gunter Fuchs. Abstract. It is well-known that the square principle $\square_\lambda$ entails the existence of a non-reflecting stationary subset of $\lambda^+$, whereas the weak square principle $\square^*_\lambda$ does not. Here we show that if $\mu^{cf(\lambda)}<\lambda$ for all $\mu<\lambda$, … Continue reading
Posted in Publications, Squares and Diamonds
Tagged 03E05, 03E35, 03E57, Diamond, Forcing Axioms, stationary reflection, weak square
Leave a comment
A forcing axiom deciding the generalized Souslin Hypothesis
Joint work with Chris Lambie-Hanson. Abstract. We derive a forcing axiom from the conjunction of square and diamond, and present a few applications, primary among them being the existence of super-Souslin trees. It follows that for every uncountable cardinal $\lambda$, … Continue reading
Posted in Publications, Souslin Hypothesis
Tagged 03E05, 03E35, 03E57, Diamond, Forcing Axioms, Souslin Tree, square, super-Souslin tree
1 Comment
Bell’s theorem on the cardinal invariant $\mathfrak p$
In this post, we shall provide a proof to a famous theorem of Murray Bell stating that $MA_\kappa(\text{the class of }\sigma\text{-centered posets})$ holds iff $\kappa<\mathfrak p$. We commence with defining the cardinal invariant $\mathfrak p$. For sets $A$ and $B$, … Continue reading
Bell’s theorem on the cardinal invariant $\mathfrak p$
In this post, we shall provide a proof to a famous theorem of Murray Bell stating that $MA_\kappa(\text{the class of }\sigma\text{-centered posets})$ holds iff $\kappa<\mathfrak p$. We commence with defining the cardinal invariant $\mathfrak p$. For sets $A$ and $B$, … Continue reading