I need help finding a good book on math logic and set theory.

[readmoreoften]

I'm working on my dissertation and one of the philosophers I'm writing on bases his analyses on set theory. I've really become interested but I have a poor math background (I stopped at Trig). Can anyone suggest a good book on Mathematical Logic for beginners, and then a book connecting Math Logic with Set Theory?

Thanks in advance!

[Davis_X_Machina]

1. Go over to Dover Publications...

....I've found them helpful, cheap and cheerful.

Lots of choices.

[readmoreoften]

4. Cool! Thanks so much! /nt

[kestrel91316]

2. You don't need math or logic. All you need is the bible.

:P

[bananas]

3. Which philospher? nt

[readmoreoften]

5. Alain Badiou's "Being and Event"

I'm actually looking at his Ethics and Metapolitics, but since he very well may be on my dissertation committee, I am afraid to look like an idiot. (Even though when it comes to math I am completely untutored.)

He bridges analytic and continental philosophy.

[bananas]

9. That was fun

I looked up the wiki entry for Alain Badiou

http://en.wikipedia.org/wiki/Alain_Badiou

This situation of being and the rupture which characterizes the event are thought in terms of set theory, and specifically Zermelo–Fraenkel set theory (with the axiom of choice), to which Badiou accords a fundamental role in a manner quite distinct from the majority of either mathematicians or philosophers.

and clicked the link for "Zermelo–Fraenkel set theory"

http://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory

For an ongoing derivation of a great deal of ordinary mathematics using ZFC, see the Metamath online project.

The Metamath project sounded interesting so I clicked on that

http://us.metamath.org/

Metamath Proof Explorer - Constructs mathematics from scratch, starting from ZFC set theory axioms. Over 6,000 proofs. Updated 26-Jul-2006.
...

clicked on "Metamath Proof Explorer" and noticed the line:

http://us.metamath.org/mpegif/mmset.html
...
Reading Suggestions
...

clicked on "Reading Suggestions"

http://us.metamath.org/mpegif/mmset.html#read

Reading Suggestions Logic and set theory provide a foundation for all of mathematics. One possible way to start to learn about them is to use the Metamath Proof Explorer in conjunction with one or more textbooks listed in the Bibliography of the next section. The textbooks provide a motivation for what we are doing, whereas the Metamath Proof Explorer lets you see in detail all hidden and implicit steps. Most standard theorems are accompanied by citations. Some closely followed texts in the Metamath Proof Explorer are listed below. While these aren't always the best books for beginners (if you have better suggestions, let me know), it will be easier to acquire a "high-level" understanding of some of the Metamath Proof Explorer proofs if you consult them while studying the proofs.

To start with, I would suggest Margaris (now available in a Dover edition, it is inexpensive and reasonably readable for beginners, once you learn the archaic notation that uses dots in place of parentheses) and Quine (it also uses the archaic dot notation, but it is wonderfully written and a pleasure to read; the first part on virtual classes is a must-read if you want to understand the class variables we use).

# Axioms of propositional calculus - Margaris.
# Theorems of propositional calculus - Whitehead and Russell.
# Axioms of predicate calculus - Megill (System S3' in the article referenced).
# Theorems of pure predicate calculus - Margaris.
# Theorems of equality and substitution - Monk2, Tarski, Megill.
# Axioms of set theory - Bell and Machover.
# Virtual classes in set theory (our class builder notation and our purple class variables) - Quine.
# Development of set theory - Takeuti and Zaring.
# Construction of real and complex numbers - Gleason
# Theorems about real numbers - Apostol

Then I went to the Dover link posted by Davis_X_Machina above,
and searched for Margaris:

http://store.doverpublications.com/by-subject-science-and-mathematics-mathematics-logic.html

First Order Mathematical Logic
by Angelo Margaris
Undergraduate-level introduction covers set theory, statement and predicate calculus, first-order theories, completeness theorem, Godel’s incompleteness theorem, much more. Exercises. Bibliography.
Our Price $11.95

That's not exactly the same title as the one on the Metamath list,
but it sounds like it covers exactly the areas you want:

http://store.doverpublications.com/0486662691.html

Well-written undergraduate-level introduction begins with symbolic logic and set theory, followed by presentation of statement calculus and predicate calculus. First-order theories are discussed in some detail, with special emphasis on number theory. After a discussion of truth and models, the completeness theorem is proved. "...an excellent text."—Mathematical Reviews. Exercises. Bibliography.

[global1]

6. George W. Bush Recommends "My Pet Goat" .......

he claims the pages are number consecutively and he thinks that's logical and they are a set because all those pages use numbers.

[readmoreoften]

7. His genius IS scary sometimes.

All pages do use the same number system. In fact, I've never seen a children's book where the numbered pages were not in numerical order. George Bush very well may be onto something. Will his genius ever cease????

[Salviati]

8. Another good place to start: Mathworld

http://mathworld.wolfram.com/

Depending on what you need to know, you might find the information online there, if not, it has tons of referances to the books relevent to each topic...

http://mathworld.wolfram.com/SetTheory.html

[bemildred]

10. Mathematical Logic, Introduction

http://www.ltn.lv/~podnieks/mlog/ml.htm

[readmoreoften]

11. Thanks so much this is really great!

Online and free :hi:

[bemildred]

12. I thought it was fairly well done too.

It's a difficult subject to do "introductions" to. If you get that far the stuff on completeness and computability theory is fascinating.