I have been asked to be part of the Scientific committee for the sixth Young set theory workshop, to be held in Piamonte, Italy, during a week in Spring 2013. The other members of the committee are Matteo Viale (chair), Asgard Tornquist, Sean Cox, and Andrew Brooke-Taylor.

James Cummings – Large cardinals: PCF-theory and its interactions with large cardinals, forcing and -like combinatorial principles. The tutorial will focus on applications of Shelah’s PCF-theory outside cardinal arithmetic, including constructions for Jónsson algebras, strong covering lemmas, and constructions for almost-free, non-free objects.

Sy David Friedman – Forcing and combinatorial set theory: Descriptive set theory on . Assuming GCH, most of the basic notions of classical descriptive set theory generalize easily from Baire space to generalized Baire space , for an uncountable regular cardinal . But many of the theorems do not. The tutorial will discuss regularity properties and the Borel reducibility of deﬁnable equivalence relations in the generalized setting.

Su Gao – Descriptive Set Theory: Borel markers in the study of countable Borel equivalence relations. The tutorial will give an introduction to the theory of Borel markers in the study of countable Borel equivalence relations. Borel markers are important tools used to attach structures to the classes of countable Borel equivalence relations. They play a prominent role in the study of hyperﬁnite and treeable equivalence relations, and have applications in other topics such as the computation of Borel chromatic numbers.

John Steel – Inner Model Theory: Iteration Trees. The tutorial will cover the basic theory of iteration trees, and some of its applications. It starts at a basic level, deﬁning ultrapowers of models of ZFC and their properties, and tries to keep the presentation accessible to anyone who has taken a graduate-level course in set theory. (In particular, no background in inner model theory will be assumed.)

I will add more details as they are decided, we expect to invite five post doctoral researchers to give one hour talks. For now, here are the links to the previous workshops:

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3 Responses to Upcoming: 6th Young set theory workshop

This is a very interesting question (and I really want to see what other answers you receive). I do not know of any general metatheorems ensuring that what you ask (in particular, about consistency strength) is the case, at least under reasonable conditions. However, arguments establishing the proof theoretic ordinal of a theory $T$ usually entail this. You […]

This is false; take a look at https://en.wikipedia.org/wiki/Analytic_set for a quick introduction. For details, look at Kechris's book on Classical Descriptive Set Theory. There you will find also some information on the history of this result, how it was originally thought to be true, and how the discovery of counterexamples led to the creation of desc […]

This is open. In $L(\mathbb R)$ the answer is yes. Hugh has several proofs of this, and it remains one of the few unpublished results in the area. The latest version of the statement (that I know of) is the claim in your parenthetical remark at the end. This gives determinacy in $L(\mathbb R)$ using, for example, a reflection argument. (I mentioned this a wh […]

A classical reference is Hypothèse du Continu by Waclaw Sierpiński (1934), available through the Virtual Library of Science as part of the series Mathematical Monographs of the Institute of Mathematics of the Polish Academy of Sciences. Sierpiński discusses equivalences and consequences. The statements covered include examples from set theory, combinatorics, […]

There is a new journal of the European Mathematical Society that seems perfect for these articles: EMS Surveys in Mathematical Sciences. The description at the link reads: The EMS Surveys in Mathematical Sciences is dedicated to publishing authoritative surveys and high-level expositions in all areas of mathematical sciences. It is a peer-reviewed periodical […]

You may be interested in the following paper: Lorenz Halbeisen, and Norbert Hungerbühler. The cardinality of Hamel bases of Banach spaces, East-West Journal of Mathematics, 2, (2000) 153-159. There, Lorenz and Norbert prove a few results about the size of Hamel bases of arbitrary infinite dimensional Banach spaces. In particular, they show: Lemma 3.4. If $K\ […]

You just need to show that $\sum_{\alpha\in F}\alpha^k=0$ for $k=0,1,\dots,q-2$. This is clear for $k=0$ (understanding $0^0$ as $1$). But $\alpha^q-\alpha=0$ for all $\alpha$ so $\alpha^{q-1}-1=0$ for all $\alpha\ne0$, and the result follows from the Newton identities.

Nice question. Let me first point out that the Riemann Hypothesis and $\mathsf{P}$-vs-$\mathsf{NP}$ are much simpler than $\Pi^1_2$: The former is $\Pi^0_1$, see this MO question, and the assertion that $\mathsf{P}=\mathsf{NP}$ is a $\Pi^0_2$ statement ("for every code for a machine of such and such kind there is a code for a machine of such other kind […]

For brevity's sake, say that a theory $T$ is nice if $T$ is a consistent theory that can interpret Peano Arithmetic and admits a recursively enumerable set of axioms. For any such $T$, the statement "$T$ is consistent" can be coded as an arithmetic statement (saying that no number codes a proof of a contradiction from the axioms of $T$). What […]

Since this page is the first google hit for “Young Set Theory 2013”, I thought I’d link here to the webpage for the conference that is now up:

http://www2.dm.unito.it/paginepersonali/viale/YST2013/yst2013-home.html

Also note that registration is open until the end of February.

Thanks Andrew, that reminds me I need to post an update. Why don’t you post a link on G+ meanwhile?

Sorry – that’s a good idea but I only just saw it, and I see that you beat me to it!