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- A strong form of König’s lemma October 21, 2017
- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- Generalizations 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

### Keywords

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

# Tag Archives: Shelah’s Strong Hypothesis

## 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, 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