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regressive Souslin tree Intersection model Sakurai's Bell inequality Forcing Greatly Mahlo higher Baire space Nonspecial tree Uniformly coherent Prevalent singular cardinals middle diamond Chromatic number Shelah's Strong Hypothesis Small forcing Prikry-type forcing Martin's Axiom Cohen real OCA ZFC construction Slim tree Subnormal ideal Ascent Path Almost Souslin S-Space Generalized Clubs Poset weak diamond Fat stationary set incompactness Well-behaved magma full tree b-scale Large Cardinals Selective Ultrafilter Strongly Luzin set Subtle tree property Cardinal function polarized partition relation Erdos-Hajnal graphs square principles Filter reflection Minimal Walks Successor of Singular Cardinal Ineffable cardinal Amenable C-sequence Generalized descriptive set theory xbox stick Partition Relations stationary hitting Antichain GMA Singular Density Ramsey theory over partitions weak square Mandelbrot set tensor product graph Fodor-type reflection positive partition relation Souslin Tree Forcing Axioms Hedetniemi's conjecture Cardinal Invariants Singular cofinality Subadditive Strong coloring unbounded function indecomposable ultrafilter weak Kurepa tree Local Club Condensation. Weakly compact cardinal Lipschitz reduction Erdos Cardinal Universal Sequences sap Distributive tree Analytic sets Knaster and friends Almost countably chromatic Was Ulam right Vanishing levels Diamond for trees super-Souslin tree Microscopic Approach Chang's conjecture PFA(S)[S] Dushnik-Miller Dowker space reflection principles Almost-disjoint family Reflecting stationary set Coherent tree Singular cardinals combinatorics P-Ideal Dichotomy Open Access AIM forcing Ostaszewski square PFA Sigma-Prikry Countryman line L-space Constructible Universe club_AD diamond star strongly bounded groups Non-saturation Whitehead Problem O-space Strongly compact cardinal ccc Kurepa Hypothesis Fast club Square-Brackets Partition Relations Commutative projection system Rock n' Roll Rado's conjecture square Ulam matrix Club Guessing Subtle cardinal Parameterized proxy principle very good scale Luzin set Foundations approachability ideal free Souslin tree specializable Souslin tree Diamond Aronszajn tree projective Boolean algebra Closed coloring Axiom R transformations countably metacompact 54G20 free Boolean algebra Precaliber Respecting tree Successor of Regular Cardinal Diamond-sharp Absoluteness Iterated forcing Knaster Uniformization coloring number C-sequence Jonsson cardinal Hereditarily Lindelöf space nonmeager set Reduced Power HOD Commutative cancellative semigroups Uniformly homogeneous Rainbow sets Sierpinski's onto mapping principle stationary reflection Postprocessing function SNR Hindman's Theorem
Tag Archives: 03E04
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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On topological spaces of singular density and minimal weight
Abstract: We introduce a weakening of the Generalized Continuum Hypothesis, which we will refer to as the Prevalent Singular cardinals Hypothesis (PSH), and show it implies that every topological space of density and weight $\aleph_{\omega_1}$ is not hereditarily Lindelöf. The assumption … Continue reading
A topological reflection principle equivalent to Shelah’s strong hypothesis
Abstract: We notice that Shelah’s Strong Hypothesis (SSH) is equivalent to the following reflection principle: Suppose $\mathbb X$ is an (infinite) first-countable space whose density is a regular cardinal, $\kappa$. If every separable subspace of $\mathbb X$ is of cardinality at most … Continue reading
Posted in Compactness, Publications, Topology
Tagged 03E04, 03E65, 54G15, Open Access, Shelah's Strong Hypothesis
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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
On the consistency strength of the Milner-Sauer conjecture
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 conjecture is consistent and known … 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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