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- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- Genearlizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
- Happy new jewish year! September 24, 2014
- Square principles April 19, 2014
- Partitioning the club guessing January 22, 2014

### Keywords

Microscopic Approach Chromatic number Square-Brackets Partition Relations b-scale Poset Fast club very good scale Singular Density Knaster PFA(S)[S] 20M14 Almost countably chromatic diamond star Successor of Regular Cardinal Slim tree Kurepa Hypothesis Forcing Axioms Fat stationary set Forcing Whitehead Problem Constructible Universe Parameterized proxy principle Generalized Clubs Universal Sequences Foundations Ostaszewski square Dushnik-Miller Club Guessing middle diamond Cohen real Selective Ultrafilter Weakly compact cardinal L-space Axiom R stationary reflection square Large Cardinals Cardinal function Rado's conjecture P-Ideal Dichotomy Non-saturation stationary hitting Coherent tree Rock n' Roll Hedetniemi's conjecture coloring number Singular cardinals combinatorics Prikry-type forcing Hereditarily Lindelöf space Singular Cofinality Erdos-Hajnal graphs Partition Relations Small forcing HOD xbox weak square Cardinal Invariants incompactness Stevo Todorcevic Almost Souslin Singular coﬁnality Fodor-type reflection Diamond ccc Chang's conjecture Reduced Power Shelah's Strong Hypothesis approachability ideal Jonsson cardinal Souslin Tree Absoluteness polarized partition relation OCA Ascent Path free Boolean algebra Aronszajn tree projective Boolean algebra Uniformization weak diamond Martin's Axiom Minimal Walks 11P99 Rainbow sets 05A17 tensor product graph reflection principles Almost-disjoint famiy Commutative cancellative semigroups Erdos Cardinal sap Successor of Singular Cardinal Prevalent singular cardinals Mandelbrot set PFA S-Space Hindman's Theorem Antichain Sakurai's Bell inequality 05D10

# Tag Archives: Shelah’s Strong Hypothesis

## Logic in Hungary 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, 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

## 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