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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

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

# 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