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Nonspecial tree Forcing weak diamond specializable Souslin tree Uniformly homogeneous Constructible Universe diamond star OCA Ascending path Ineffable cardinal Generalized descriptive set theory club_AD Prevalent singular cardinals Subtle tree property PFA Knaster and friends Analytic sets Ostaszewski square Rado's conjecture Intersection model Chang's conjecture Weakly compact cardinal coloring number Hindman's Theorem C-sequence Open Access Vanishing levels Filter reflection Fat stationary set square principles Small forcing Prikry-type forcing Parameterized proxy principle sap Almost Souslin Ascent Path Antichain nonmeager set Rock n' Roll Amenable C-sequence Diamond-sharp Monotonically far full tree Countryman line Jonsson cardinal AIM forcing super-Souslin tree polarized partition relation Subnormal ideal Entangled linear order Successor of Singular Cardinal Coherent tree Commutative projection system weak square Was Ulam right? Distributive tree b-scale Closed coloring Forcing Axioms positive partition relation PFA(S)[S] Subtle cardinal Hedetniemi's conjecture Reflecting stationary set Strongly compact cardinal Universal Sequences ccc Lipschitz reduction weak Kurepa tree Successor of Regular Cardinal Strong coloring Shelah's Strong Hypothesis tensor product graph stationary hitting SNR stick O-space Singular Density P-Ideal Dichotomy Aronszajn tree Ulam matrix Axiom R Microscopic Approach Well-behaved magma Non-saturation Respecting tree Fodor-type reflection Almost countably chromatic Singular cardinals combinatorics Large Cardinals projective Boolean algebra Reduced Power Minimal Walks Local Club Condensation. Martin's Axiom free Boolean algebra ZFC construction HOD Partition Relations Sakurai's Bell inequality Slim tree Commutative cancellative semigroups transformations Dowker space Greatly Mahlo 54G20 Strongly Luzin set Iterated forcing Subadditive Uniformly coherent Luzin set Kurepa Hypothesis Diamond for trees strongly bounded groups middle diamond Diamond unbounded function Singular cofinality incompactness Souslin Tree stationary reflection Precaliber Cardinal function Rainbow sets Uniformization L-space approachability ideal Sierpinski's onto mapping principle Sigma-Prikry Cardinal Invariants S-Space Hereditarily Lindelöf space Dushnik-Miller free Souslin tree Knaster very good scale xbox Selective Ultrafilter Absoluteness Poset higher Baire space Square-Brackets Partition Relations Almost-disjoint family Whitehead Problem reflection principles Ramsey theory over partitions Club Guessing GMA Generalized Clubs regressive Souslin tree Foundations Forcing with side conditions Partition relations for trees perfectly normal Mandelbrot set countably metacompact Erdos-Hajnal graphs Cohen real indecomposable filter Chromatic number Erdos Cardinal Postprocessing function Interval topology on trees square Fast club
Author Archives: Assaf Rinot
Workshop on Set Theory and its Applications, February 2007
These are the slides of a talk given at the Workshop on Set Theory and its Applications workshop (Weizmann Institute, February 19, 2007). Talk Title: Nets of spaces having singular density Abstract: The weight of a topological space X is the … Continue reading
Annual conference of the IMU, May 2006
This talk was given at the 2006 Annual Conference of the Israel Mathematical Union (Neve Ilan, 25-26 May 2006). Talk Title: The Milner-Sauer conjecture and covering numbers Abstract: In their paper from 1981, after learning about Pouzet‘s theorem that any poset of singular cofinality mush contain … Continue reading
Posted in Invited Talks
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Logic in Hungary, August 2005
These are the slides of a contributed talk given at the Logic in Hungary 2005 meeting (Budapest, 5–11 August 2005). Talk Title: On the consistency strength of the Milner-Sauer Conjecture Abstract: In their paper from 1981, after learning about Pouzet‘s theorem that any … Continue reading
Posted in Contributed Talks
Tagged Antichain, Shelah's Strong Hypothesis, Singular cofinality
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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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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
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
Transforming rectangles into squares, with applications to strong colorings
Abstract: It is proved that every singular cardinal $\lambda$ admits a function $\textbf{rts}:[\lambda^+]^2\rightarrow[\lambda^+]^2$ that transforms rectangles into squares. That is, whenever $A,B$ are cofinal subsets of $\lambda^+$, we have $\textbf{rts}[A\circledast B]\supseteq C\circledast C$, for some cofinal subset $C\subseteq\lambda^+$. As a … Continue reading
