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xbox Greatly Mahlo Chang's conjecture Luzin set Hereditarily Lindelöf space Antichain Martin's Axiom countably metacompact Aronszajn tree Almost countably chromatic higher Baire space SNR Almost-disjoint family Souslin Tree club_AD specializable Souslin tree Ostaszewski square positive partition relation Dushnik-Miller weak Kurepa tree diamond star weak diamond free Boolean algebra Knaster Microscopic Approach Vanishing levels Strong coloring Amenable C-sequence Hindman's Theorem incompactness Singular Density S-Space b-scale Sakurai's Bell inequality Hedetniemi's conjecture Nonspecial tree Partition Relations Postprocessing function Sigma-Prikry Generalized Clubs Well-behaved magma Cardinal function Almost Souslin Filter reflection Parameterized proxy principle Ramsey theory over partitions Uniformization Weakly compact cardinal Coherent tree full tree Constructible Universe ccc Rado's conjecture Analytic sets stationary reflection Successor of Singular Cardinal regressive Souslin tree projective Boolean algebra Poset Local Club Condensation. Successor of Regular Cardinal Kurepa Hypothesis Singular cardinals combinatorics Reduced Power polarized partition relation Jonsson cardinal tensor product graph L-space Rock n' Roll super-Souslin tree HOD Ineffable cardinal Dowker space Mandelbrot set free Souslin tree Diamond-sharp Foundations Large Cardinals indecomposable ultrafilter Absoluteness Selective Ultrafilter Forcing Uniformly homogeneous strongly bounded groups Iterated forcing Prikry-type forcing Cohen real Was Ulam right Subtle cardinal Slim tree Precaliber Generalized descriptive set theory Whitehead Problem Ascent Path middle diamond stationary hitting Subtle tree property Subadditive Closed coloring sap square Universal Sequences Fodor-type reflection AIM forcing Reflecting stationary set Commutative cancellative semigroups Diamond Small forcing 54G20 Erdos-Hajnal graphs Sierpinski's onto mapping principle nonmeager set reflection principles Rainbow sets Strongly Luzin set Distributive tree O-space Chromatic number weak square Fat stationary set Subnormal ideal Minimal Walks Prevalent singular cardinals PFA(S)[S] Diamond for trees unbounded function very good scale P-Ideal Dichotomy stick Erdos Cardinal GMA PFA Singular cofinality Square-Brackets Partition Relations Knaster and friends approachability ideal Lipschitz reduction C-sequence ZFC construction Open Access Shelah's Strong Hypothesis Uniformly coherent Non-saturation coloring number Axiom R Club Guessing transformations OCA Cardinal Invariants square principles Fast club Forcing Axioms Ulam matrix
Tag Archives: Prikry-type forcing
Sigma-Prikry forcing II: Iteration Scheme
Joint work with Alejandro Poveda and Dima Sinapova. Abstract. In Part I of this series, we introduced a class of notions of forcing which we call $\Sigma$-Prikry, and showed that many of the known Prikry-type notions of forcing that centers … Continue reading
Sigma-Prikry forcing I: The Axioms
Joint work with Alejandro Poveda and Dima Sinapova. Abstract. We introduce a class of notions of forcing which we call $\Sigma$-Prikry, and show that many of the known Prikry-type notions of forcing that centers around singular cardinals of countable cofinality … Continue reading
More notions of forcing add a Souslin tree
Joint work with Ari Meir Brodsky. Abstract. An $\aleph_1$-Souslin tree is a complicated combinatorial object whose existence cannot be decided on the grounds of ZFC alone. But 15 years after Tennenbaum and independently Jech devised notions of forcing for introducing … Continue reading
Prikry forcing may add a Souslin tree
A celebrated theorem of Shelah states that adding a Cohen real introduces a Souslin tree. Are there any other examples of notions of forcing that add a $\kappa$-Souslin tree? and why is this of interest? My motivation comes from a … Continue reading
Prikry Forcing
Recall that the chromatic number of a (symmetric) graph $(G,E)$, denoted $\text{Chr}(G,E)$, is the least (possible finite) cardinal $\kappa$, for which there exists a coloring $c:G\rightarrow\kappa$ such that $gEh$ entails $c(g)\neq c(h)$. Given a forcing notion $\mathbb P$, it is … Continue reading