Hi @All

Which book are we following?

oops, saw the message in MathChat just now!

Kunen's Set Theory: An Introduction To Independence Proofs. There is apparently a 2011 new edition of that book, but I only have a copy of the edition from the 80s so I don't know how many differences are there between the two

Still, it probably would not hurt to put it into room description.

as soon as I work out how to do that :P

room topic changed to Set Theory Study Group: We're following Kunen's book "Set Theory: An Introduction To Independence Proofs". Request to join if you're interested (no tags)

The preface to the newer edition starts: "This book is a total rewrite of the author's Set Theory: An Introduction to Independence Proofs, first published in 1980."

relevant SE question

@AlessandroCodenotti nice find

Here is preface from the newer edition: i.sstatic.net/98NtU.png

The author expands there on "why the rewrite was needed".

It's about two paragraphs, so probably too long to copy here in full.

Hm, the second edition seems more modern in the choice of topics, but the SE answers mention that the first covers the basics better (and we'll probably have people with very little previous knowledge of set theory here)

"Second, model-theoretic methods have become increasingly prevalent in mathematical arguments. ... But now, anyone doing research in the more set-theoretic areas of topology and analysis has learned basic model theory and knows how to apply model-theoretic techniques to set-theoretic problems. So, the present book describes these techniques in Chapter I, as part of a review of basic logic, and then in later chapters applies these techniques to mathematical theorems ..."

I guess that even if somebody does not have the newer edition, it probably can be found online...?

It can (which book can't?)

The new edition's title is just "Set Theory" by the way

I'll have to leave.

We will see what other people interested in this say, but I think that newer edition might be better. (Probably the author thinks it's an improvement, otherwise they wouldn't write the new version.)

makes sense. There were some people from the US who were interested, I guess they'll join us later

@AlessandroCodenotti Personally, I'd guess that somebody who wants to read a book about forcing and independence proofs already has at least some background in basics of set theory.

(Concerning your remark: "we'll probably have people with very little previous knowledge of set theory here".)

Although I do not really know how much set theory is expected for somebody who wants to start learning forcing.

@AlessandroCodenotti @MartinSleziak Is Halmos' Naive Set Theory a good measure of the requisites going in?

What about utter noobs like me who don't have a formal training in Undergrad level Set Theory/Logic, is there scope to participate in this group?

I will copy here what the author says in the section 0.2 Prerequisities (in the newer edition):

It is assumed that you know basic set theory. This includes a knowledge of ZFC and the development, within ZFC, of basic properties of the ordinals and the infinite cardinals. We also assume some rudimentary knowledge of model theory and recursion theory. In particular, you should have seen formal logic

and the terminology $\Gamma \vdash \varphi$ used to mean that there is a formal proof of $\varphi$ from $\Gamma$; here, $\Gamma$ is a set of logical axioms (such as ZFC) and $\varphi$ is a logical sentence.

Logic text vary as to the precise definition of "logical sentence" and "formal proof", but you should be aware that these notions are decidable; that is, there is an algorithm that will input a finite symbolic object and tell you whether it is a logical sentence, or an axiom of ZFC, or a formal proof.

You should also know that $\Gamma \vdash \varphi$ is equivalent to the semantic notion $\Gamma\models\varphi$ ($\varphi$ is true in all models of $\Gamma$) by the Soundness and Completeness Theorems.

The prerequisite material is usually covered in a beginning graduate level course in logic. Everything needed can be found in the author's [57]. However, much of [57] is not relevant here, and many readers will have learned the equivalent material from other such as [28, 29, 53, 69, 71, 89]. Chapter I contains a summary of what is important.

This chapter stresses basic logic issues, such as properties of models of set theory, since these are sometimes skimmed over in beginning courses, while it omits proofs of technical results such as Konig's Theorem 1.13.12 ($\operatorname{cf}(\kappa^\lambda)>\lambda$), which such courses usually do cover.

We also assume some knowledge of elementary topology and analysis. This is not strictly necessary for understanding the proof that CH is independent of ZFC, but, as indicated in the previous section, the main reason for being interested in independence results is their relevance to these subjects, so we try to integrate examples from topology and analysis into the text.

@LastIronStar I am not sure, but perhaps the above might help to estimate how much of the knowledge of set theory is needed for reading this book.

The [57] mentioned in that section is Kunen's "The Foundations of Mathematics"

Personally, when I read the above, I see that I am a bit hazy on the basics of model theory. (I have been taught a course in this subject, but it was a long time ago.)

However, this is mainly question for Alessandro - since he suggested the group, the question is what he has in mind (as far as the pace or the level of participants is concerned).

That paragraph makes me wonder whether I have the prerequisites to read it, especially concerning Model Theory of which I know next to nothing

However, if it turns out that somebody is missing some background, I guess it can be discussed a bit here (or in other chat rooms, such as Set Theory or Logic) or on the main site.

I guess it is not very likely that we find several users who are roughly at the same level and who all want to participate in this. So probably it is to be expected that some of us will have to study more in some parts - while others might be already familiar with them.

"The Foundations of Mathematics" seems to be extremely accessible, we could also go through the first 2 chapters (Set Theory and Model Theory) at a very fast pace and then work on the other book

The sounds like a plan.