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I am looking for study and beginner material to study mathematical logic. I understand that it is a very broad topic but I would like to know what the best path there is to learning mathematical logic. Where should one start? What are the best resources? If someone could paint a time line of events that should take place in order to gain a good understanding of mathematical logic, that would be fantastic. I have seen this question but it does not give the depth I require.

Community
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Jeel Shah
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  • What's wrong with, for instance, Peter Smith's answer. – Git Gud Apr 27 '13 at 17:08
  • @GitGud I had not seen that but it looks to be comprehensive. So are the resources mentioned in the guide the best or really good? I only say this because I am completely new to studying logic and I want the resources to explain step-by-step the formulations and the reasoning. I find that some of the resources move too quickly or expect you to know a host of things before you can learn the said topic. – Jeel Shah Apr 27 '13 at 17:12
  • To be honest I don't know, I haven't gone through Peter Smith's material yet. You should ping (or e-mail) him. – Git Gud Apr 27 '13 at 17:16
  • gekkostate: see Peter Smith's site logicmatters.net. Yes, Peter Smith's work is a great resource. – amWhy Apr 27 '13 at 17:17

2 Answers2

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  1. For a heavily annotated and detailed Guide to teaching yourself logic by a selection from the many many available books, try my Teach Yourself Logic at http://www.logicmatters.net/students/tyl/ It aims precisely to enable a student to move on "step-by-step". [Added: The current version is Beginning Mathematical Logic: A Study Guide, freely downloadable at the same URL, and also a v. cheap pbk.]

  2. I'm not sure quite what you mean by "paint[ing] a time line of events that should take place in order to gain a good understanding of mathematical logic"; but TYL does have a crude map of the way areas of mathematical logic relate to each other which might help.

Peter Smith
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  • I am reading your .pdf right now and it contains exactly what I am looking for. The timeline, I am talking about is the correct steps that should be taken to learn logic. I find that I jump from one concept to another have holes but the tree on page 9 of your .pdf is exactly what I was looking for. To learn "baby logic" then first order logic etc. So, thank you. – Jeel Shah Apr 27 '13 at 18:32
  • Glad you think it is what you are looking for! – Peter Smith Apr 27 '13 at 18:39
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I want to give an alternative approach to Peter Smith selection of books, what IMO is more aimed to philosophers than mathematicians.

IMHO the best introductory book of mathematical logic that you can read is the first two (or maybe three) chapters of A concise introduction to mathematical logic of Wolfgang Rautenberg.

Also it is very hard to beat, in rigor, the first two chapters of Introduction of mathematical logic of Elliot Mendelson or the first chapters of Mathematical logic of Tourlakis.

The big problem that I found in almost all introductory books to mathematical logic is that when the authors try to make things easier (as an introductory text demand) they do just wrong, appealing to informal reasons to show how to be formal!

Masacroso
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