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