Comment author:Vladimir_M
06 October 2010 12:52:21AM
6 points
[-]

Also, here are some excellent online resources for those wiling to plunge into mathematical logic, math foundations, and computability theory:

A two-part online text by Karlis Podnieks: Introduction to Mathematical Logic and What is Mathematics: Gödel's Theorem and Around. Written in ugly plain text, and with some bits still incomplete, but on the upside, extremely well-written and probably as readable as a rigorous text on this topic could ever hope to be. (The text is also peppered with the author's philosophical opinions, but you can skip those if you don't like them.)

Stephen Cook's lecture notes in computability and logic. A rigorous build-up to Goedel's incompleteness theorems with minimal background knowledge assumed, which introduces the basics of mathematical logic and computability theory on the way. The text is very readable and surprisingly short considering the whole range of topics covered.

This could take a while to go through, but despite cousin_it's optimistic estimates, I would say that working through at least one of these texts would be necessary before you can discuss topics such as Loeb's theorem with any real understanding. If you've never studied math, or if you've studied it only in a very applied and non-theoretical way, the greatest problem will be getting used to the necessary way of thinking.

## Comments (12)

ControversialAlso, here are some excellent online resources for those wiling to plunge into mathematical logic, math foundations, and computability theory:

A two-part online text by Karlis Podnieks:

Introduction to Mathematical LogicandWhat is Mathematics: Gödel's Theorem and Around. Written in ugly plain text, and with some bits still incomplete, but on the upside, extremely well-written and probably as readable as a rigorous text on this topic could ever hope to be. (The text is also peppered with the author's philosophical opinions, but you can skip those if you don't like them.)Stephen Cook's lecture notes in computability and logic. A rigorous build-up to Goedel's incompleteness theorems with minimal background knowledge assumed, which introduces the basics of mathematical logic and computability theory on the way. The text is very readable and surprisingly short considering the whole range of topics covered.

This could take a while to go through, but despite cousin_it's optimistic estimates, I would say that working through at least one of these texts would be necessary before you can discuss topics such as Loeb's theorem with any real understanding. If you've never studied math, or if you've studied it only in a very applied and non-theoretical way, the greatest problem will be getting used to the necessary way of thinking.

*2 points [-]I usually recommend Gödel Without Tears. At least one person has used it to learn logic by my suggestion. Took them a couple weeks.