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