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Intersection model Jonsson cardinal Martin's Axiom club_AD Rainbow sets ccc Sierpinski's onto mapping principle Chang's conjecture Forcing P-Ideal Dichotomy Axiom R Subtle tree property Successor of Regular Cardinal PFA 54G20 Open Access Square-Brackets Partition Relations specializable Souslin tree Strong coloring Local Club Condensation. Filter reflection Dushnik-Miller Commutative cancellative semigroups ZFC construction positive partition relation countably metacompact Non-saturation Shelah's Strong Hypothesis Vanishing levels indecomposable filter Uniformization Partition relations for trees Subnormal ideal Ascending path square Singular Density S-Space Diamond-sharp stationary hitting Whitehead Problem Ulam matrix Cardinal Invariants free Boolean algebra approachability ideal transformations incompactness Prevalent singular cardinals Hindman's Theorem Uniformly coherent Minimal Walks weak diamond Countryman line b-scale stick SNR Lipschitz reduction Uniformly homogeneous Nonspecial tree Ostaszewski square Large Cardinals diamond star Reflecting stationary set regressive Souslin tree weak square Ascent Path Small forcing Almost countably chromatic Forcing with side conditions GMA Greatly Mahlo Iterated forcing Fast club unbounded function Erdos Cardinal Subtle cardinal Monotonically far Reduced Power Singular cardinals combinatorics reflection principles Foundations Ineffable cardinal Knaster super-Souslin tree PFA(S)[S] xbox Parameterized proxy principle HOD Chromatic number Club Guessing polarized partition relation strongly bounded groups Almost-disjoint family Aronszajn tree Mandelbrot set sap Weakly compact cardinal Luzin set Generalized Clubs Hereditarily Lindelöf space Slim tree Erdos-Hajnal graphs Dowker space Selective Ultrafilter Strongly Luzin set nonmeager set Kurepa Hypothesis Coherent tree Precaliber Souslin Tree Sakurai's Bell inequality Commutative projection system Respecting tree Forcing Axioms Sigma-Prikry very good scale Entangled linear order Distributive tree Singular cofinality projective Boolean algebra Absoluteness L-space Antichain O-space Cohen real Subadditive Generalized descriptive set theory Successor of Singular Cardinal AIM forcing Knaster and friends Constructible Universe square principles Almost Souslin Fat stationary set Strongly compact cardinal middle diamond Rado's conjecture Well-behaved magma Universal Sequences Cardinal function coloring number Analytic sets Closed coloring tensor product graph Was Ulam right? Ramsey theory over partitions C-sequence Interval topology on trees higher Baire space perfectly normal full tree Microscopic Approach Rock n' Roll Diamond for trees Fodor-type reflection weak Kurepa tree Amenable C-sequence OCA Postprocessing function Partition Relations stationary reflection Poset Hedetniemi's conjecture Prikry-type forcing free Souslin tree Diamond
Tag Archives: Prikry-type forcing
A counterexample related to a theorem of Komjáth and Weiss
Joint work with Rodrigo Rey Carvalho. Abstract. In a paper from 1987, Komjath and Weiss proved that for every regular topological space $X$ of character less than $\mathfrak b$, if $X\rightarrow(\text{top }{\omega+1})^1_\omega$, then $X\rightarrow(\text{top }{\alpha})^1_\omega$ for all $\alpha<\omega_1$. In addition, … Continue reading
Posted in Partition Relations, Preprints, Topology
Tagged 03E02, 54G20, Open Access, Prikry-type forcing, ZFC construction
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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
Knaster and friends II: The C-sequence number
Joint work with Chris Lambie-Hanson. Abstract. Motivated by a characterization of weakly compact cardinals due to Todorcevic, we introduce a new cardinal characteristic, the C-sequence number, which can be seen as a measure of the compactness of a regular uncountable … 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
The eightfold way
Joint work with James Cummings, Sy-David Friedman, Menachem Magidor, and Dima Sinapova. Abstract. Three central combinatorial properties in set theory are the tree property, the approachability property and stationary reflection. We prove the mutual independence of these properties by showing … 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
Ordinal definable subsets of singular cardinals
Joint work with James Cummings, Sy-David Friedman, Menachem Magidor, and Dima Sinapova. Abstract. A remarkable result by Shelah states that if $\kappa$ is a singular strong limit cardinal of uncountable cofinality then there is a subset $x$ of $\kappa$ such … 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
