u/Impossible_Boot5113

INTRO
I'd like suggestions for both first topic(s) and book(s) for a new study group in Mathematical Logic. And/or comments on my ideas.

BACKGROUND
I'm starting a (physical/IRL) study group in Mathematical Logic with some friends, colleagues and neighbours. We're meeting in our (limited) free time, and all have jobs and (family)lifes besides the study group. I think we'll be meeting about once a month.

The purpose of the study group is to learn for fun as a hobby and share excitement of Mathematical Logic. We are not studying for an education (we have all completed our studies) or for work or some concrete project. It's just for fun :).

Our very first meeting is in a couple of weeks. After a presentation-round, we will decide on a SUBJECT and BOOK for the next period of time.

MEMBER PROFILES
We have pretty different backgrounds/profiles:
* P1 (me): Majored in Philosophy with minor in Math (1 year of pure math courses) about 10 years ago. Has started self-studying Mathematical Logic about 7 months ago, and covered: Basic naive Set Theory, Logic up to Completeness of FOL (p.150 in Enderton), some basic Model Theory (definability, un-definability, Theories, Compactness), and a little bit of Modal Logic.
* P2: An ex-ph.d. in Philosophy of Math (completed). Also doing/done some programming in free time.
* P3: An engineer (self-described "closet physicist") working with data-analysis.
* P4: A software-engineer working "in IT" with some programming (I think :)).
* P5: A comp.sci-graduate (completed) with specialty in symbolic logic. Doing a bit of self-study in Mathematical Logic.
Only P1 and P5 has self-studied Mathematical Logic (recently). But most others have a pretty high level of "Mathematical maturity".

QUESTIONS

1. What SUBJECT do you suggest for our first "project"? And what about a longer sequence of subjects for the next semester/year/years?

... I'm leaning towards COMPUTABILITY THEORY for our very first subject, since it's right at the intersection between Philosophy, Logic, Math and Computer Science. And the "lack" of training in formal logic won't be a big problem when designing Turing Machines or Unlimited Register Machines (?)

It could perhaps make sense to start with FORMAL LOGIC, but the problem is that our levels of knowledge are very different. I would rather have an exciting unifying first topic, where everybody can contribute with something and feel at home.

2. What BOOK(S)? For COMPUTABILITY THEORY I am leaning towards Cutland: "Computability". It seems good for self-study, it's not too advanced, and the engineers/comp.sci's won't feel it's "too philosophical".

I'm also thinking about:

* Weber: "Computability Theory" (seems to proceed faster than Cutland - more advanced)

* Robič: "Foundations of Computability Theory" (starts with optional long intro on foundational crisis, Hilbert's Program etc.. Has 2 tracks: One for main ideas and one optional for proofs and extra theory)

* Epstein & Carnielli: "Computability" (very friendly and "easy". More focus on Philosophical points than the other books)

... What do you suggest/think?

For a later "training course" in Logic, I'm thinking about Open Logic Project "Sets, Logic, Computation" since it's cheap, readily available, and neither too hard nor too simple. And it has a nice introduction in Set Theory for those who need that first.

Also thinking about Chiswell and Hodges "Mathematical Logic", since it's supposedly friendly and easy.

I have looked at Leary and Kristianen's "A Friendly Introduction to Mathematical Logic" but didn't really like that style.

Please give advice on good subjects/topics, good books (for the subjects) and/or general advice on cultivating a nice study group. Thanks! :)

I'm self-studying Logic and Set Theory in my free time, and I'm thinking about learning some MODAL LOGIC.

QUESTION: What books do you recommend to learn Modal Logic? What to focus on? What "routes"?

(See below for my goals and my background)

MOTIVATION: I find modal logic interesting in it's own right.

But I have also recently bought the book "SET THEORY AND THE CONTINUUM PROBLEM" by Smullyan and Fitting, where they use Modal Logic to develop FORCING (which I really want to learn some day). I think it's the system S4 they use.

And I have also bought "THE LOGIC OF PROVABILITY" by Boolos, where he uses Modal Logic to prove Gödel's Incompleteness Theorems.

I would like to be able to understand those books - so I would like my Modal Logic studies to supply the necessary prerequisites.

INTERESTS: I have found out that I really like the "deep", "big" and mindbending results. And dislike low-level grinding. I find semantics and Model Theory really interesting. But not really Proof Theory or low-level "programming" of Turing Machines.

For example I found it really boring to follow and construct low-level Turing Machines that "detect a 1" or "multiply by 2". Whereas I really liked the proof that there are functions that can't be encoded by Turing Machines (since the set of functions N->N is uncountable and the set of Turing Machines is countable).

BACKGROUND: I have a university education with a "major" in Philosophy and "minor" in math with just 1 year of pure math courses.

During the past 6 months I have begun self-studying Logic and Set Theory.

I have worked through the first 6 chapters of Button's "Set Theory: An Open Introduction" to refresh Set Theory (done almost all exercises). And then worked through the first 150 pages of Enderton's "A Mathematical Introduction to Logic" (done about 20 exercises). And read a lot of stuff on the side such as quite a bit of The Open Logic Project "Sets, Logic, Computation", the first 40 pages of Smullyan's "First Order Logic", parts of Van Dalen’s "Logic and Structure" and 120-140 pages of the "Handbook of Philosophical Logic".

And recently I have begun reading Model Theory - have read the first 45 pages of Kossak's "Model Theory for Beginners" with all inline exercises along the way.

... Now I'm thinking about what to study next after my first taste of basic Model Theory, and I'm thinking about MODAL LOGIC.

With kind regards