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Selective Ultrafilter xbox Uniformly coherent Shelah's Strong Hypothesis Sierpinski's onto mapping principle weak Kurepa tree Hedetniemi's conjecture Ramsey theory over partitions Precaliber stationary reflection Constructible Universe Ostaszewski square higher Baire space Uniformly homogeneous Hindman's Theorem nonmeager set stationary hitting Generalized Clubs b-scale Commutative cancellative semigroups Whitehead Problem Erdos-Hajnal graphs Non-saturation Reduced Power Diamond for trees 54G20 ZFC construction Rock n' Roll S-Space indecomposable filter Prikry-type forcing polarized partition relation Vanishing levels Kurepa Hypothesis Universal Sequences Rainbow sets Was Ulam right? Microscopic Approach transformations coloring number Reflecting stationary set Knaster Forcing C-sequence Almost Souslin Minimal Walks Successor of Singular Cardinal Lipschitz reduction Partition relations for trees Interval topology on trees approachability ideal Greatly Mahlo square principles Fodor-type reflection ccc Weakly compact cardinal Local Club Condensation. regressive Souslin tree Cardinal function Entangled linear order Almost countably chromatic Foundations Luzin set Fast club Monotonically far Amenable C-sequence full tree free Souslin tree projective Boolean algebra Sakurai's Bell inequality Diamond perfectly normal Ascent Path Cardinal Invariants Square-Brackets Partition Relations Filter reflection Ineffable cardinal Intersection model Coherent tree Partition Relations Axiom R Jonsson cardinal Souslin Tree Cohen real Successor of Regular Cardinal very good scale super-Souslin tree AIM forcing Generalized descriptive set theory Slim tree Poset Forcing with side conditions Forcing Axioms Chang's conjecture Prevalent singular cardinals square Fat stationary set L-space Aronszajn tree OCA Mandelbrot set tensor product graph Singular cardinals combinatorics Strongly Luzin set Nonspecial tree Almost-disjoint family O-space countably metacompact incompactness GMA Absoluteness Knaster and friends Diamond-sharp Distributive tree Dushnik-Miller Commutative projection system Closed coloring Strongly compact cardinal Countryman line Postprocessing function SNR Analytic sets Chromatic number Subtle cardinal unbounded function stick Well-behaved magma Sigma-Prikry sap Antichain Subtle tree property diamond star reflection principles Singular cofinality Singular Density Erdos Cardinal Uniformization PFA Subadditive PFA(S)[S] Respecting tree Hereditarily Lindelöf space positive partition relation Rado's conjecture P-Ideal Dichotomy strongly bounded groups Subnormal ideal Large Cardinals Ulam matrix middle diamond weak square HOD specializable Souslin tree Strong coloring weak diamond club_AD Club Guessing Dowker space Ascending path Iterated forcing free Boolean algebra Open Access Parameterized proxy principle Small forcing Martin's Axiom
Tag Archives: 03E35
A cofinality-preserving small forcing may introduce a special Aronszajn tree
Extended Abstract: Shelah proved that Cohen forcing introduces a Souslin tree; Jensen proved that a c.c.c. forcing may consistently add a Kurepa tree; Todorcevic proved that a Knaster poset may already force the Kurepa hypothesis; Irrgang introduced a c.c.c. notion … Continue reading
Posted in Publications, Squares and Diamonds
Tagged 03E04, 03E05, 03E35, Aronszajn tree, Small forcing, Successor of Singular Cardinal, weak square
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Openly generated Boolean algebras and the Fodor-type reflection principle
Joint work with Sakaé Fuchino. Abstract: We prove that the Fodor-type Reflection Principle (FRP) is equivalent to the assertion that any Boolean algebra is openly generated if and only if it is $\aleph _2$-projective. Previously it was known that this … Continue reading
Posted in Compactness, Publications
Tagged 03E35, 03E55, 03E65, 03E75, 03G05, 06E05, Axiom R, Fodor-type reflection, free Boolean algebra, projective Boolean algebra, Shelah's Strong Hypothesis, stationary reflection
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The failure of diamond on a reflecting stationary set
Joint work with Moti Gitik. Abstract: It is shown that the failure of $\diamondsuit_S$, for a subset $S\subseteq\aleph_{\omega+1}$ that reflects stationarily often, is consistent with GCH and $\text{AP}_{\aleph_\omega}$, relatively to the existence of a supercompact cardinal. This should be comapred with … Continue reading
A relative of the approachability ideal, diamond and non-saturation
Abstract: Let $\lambda$ denote a singular cardinal. Zeman, improving a previous result of Shelah, proved that $\square^*_\lambda$ together with $2^\lambda=\lambda^+$ implies $\diamondsuit_S$ for every $S\subseteq\lambda^+$ that reflects stationarily often. In this paper, for a subset $S\subset\lambda^+$, a normal subideal of … Continue reading
On guessing generalized clubs at the successors of regulars
Abstract: Konig, Larson and Yoshinobu initiated the study of principles for guessing generalized clubs, and introduced a construction of an higher Souslin tree from the strong guessing principle. Complementary to the author’s work on the validity of diamond and non-saturation … Continue reading
Antichains in partially ordered sets of singular cofinality
Abstract: In their paper from 1981, Milner and Sauer conjectured that for any poset $\mathbb P$, if $\text{cf}(\mathbb P)$ is a singular cardinal $\lambda$, then $\mathbb P$ must contain an antichain of size $\text{cf}(\lambda)$. The main result of of this … Continue reading
Posted in Publications, Singular Cardinals Combinatorics
Tagged 03E04, 03E35, 06A07, Antichain, Poset, Singular cofinality
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The Ostaszewski square, and homogeneous Souslin trees
Abstract: Assume GCH and let $\lambda$ denote an uncountable cardinal. We prove that if $\square_\lambda$ holds, then this may be witnessed by a coherent sequence $\left\langle C_\alpha \mid \alpha<\lambda^+\right\rangle$ with the following remarkable guessing property: For every sequence $\langle A_i\mid i<\lambda\rangle$ … Continue reading
Posted in Publications, Souslin Hypothesis, Squares and Diamonds
Tagged 03E05, 03E35, Club Guessing, Fat stationary set, Ostaszewski square, Souslin Tree
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