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