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in last two months , i asked many people about good text for first mathematical logic .

after that a chose some text , first order mathematical logic , angelo magrais ,

it is ok but the text uses dotty system , this system of writing is not fine for me , so i thought in changing the text and study from another text .

or , i need some essays or topics to be fammillar with dotty system ,

let us talk about the first option , changing the text ,

i read about , a concise introuduction of mathematical logic by Wolfgang Rautenberg .. and also about , mathematical logic by Ebbinghaus ..

but i read some comments says that these two text is not excellent for a first course and the learner must study first from simpler text then go to study from these text .

but i don't know what are these simpler texts ! , so , i'm very confused . i also read some first sections from , mathematical logic part 1 by Lascar and Cori .

so my question is , which texts are excellent for first course in mathematical logic ? and why ?

which topics should be covered in this first course ?

is any of the texts which i mentioned is suitable for first course or not ?

i really hope that you can help , i'm very confused about the good text - or texts - which i should start from .

thanx !

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    $\begingroup$ Using both letters in upper case and lower case would increase the readability of your question greatly. $\endgroup$
    – Michael Greinecker
    Feb 26, 2013 at 20:33
  • $\begingroup$ @MichaelGreinecker , i didn't understand well , can you make it more clear ? $\endgroup$
    – Fawzy Hegab
    Feb 26, 2013 at 20:34
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    $\begingroup$ this sentence should have started with a T. This sentence does. $\endgroup$
    – Michael Greinecker
    Feb 26, 2013 at 20:36
  • $\begingroup$ @MichaelGreinecker , You mean using capital and small letters in the right way , don't you ? $\endgroup$
    – Fawzy Hegab
    Feb 26, 2013 at 20:40
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    $\begingroup$ @MrWhy Yes. Otherwise, the question reads like a chat protocol. $\endgroup$
    – Michael Greinecker
    Feb 26, 2013 at 20:41

2 Answers 2

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One possible resource, and frequently used for a first course in mathematical logic, is Herbert Enderton's A Mathematical Introduction to Logic. It seems fitting for a first course. I very much liked the text. You can preview the text book, and its table of contents, at the given link.

Please also see this earlier post for a number of recommendations:

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  • $\begingroup$ thanx , i read the link you posted when you posted it in a comment , it will be useful , i will read it again , Do you think that Wolfgang's text or Ebbinghaus's text or Lascar and Cori 's text is suitable after finishing this text by Enderton ? or is it possible to start from them ? $\endgroup$
    – Fawzy Hegab
    Feb 26, 2013 at 20:54
  • $\begingroup$ I can definitely recommend Ebbinghaus, but I'm not as familiar with the others. Ebbinghaus is a classic. If you're interested in learning about Godel, you might want to check out Peter Smith's \logicmatters website, (I think he's given the link in an earlier answer to you), for resources. Plus, Peter Smith has authored quite a bit in this area (Godel's Incompleteness Theorem, etc.) $\endgroup$
    – amWhy
    Feb 26, 2013 at 20:56
  • $\begingroup$ ok , i think i will start the study from the text you recommended - Herbert Enderton's text : A Mathematical Introduction to Logic - with the small text which Ittay Weiss recommended . $\endgroup$
    – Fawzy Hegab
    Feb 26, 2013 at 21:04
  • $\begingroup$ i spent many time on the applications of sylow theorems . it's 3 pages but it needed Big Amount of Time . i'll start solving some exercises on sylows theorems and then reviewing chapter 3 specially and then reviewing the proofs of all important theorems - i'm from this kind of people who is very interisted in the proofs of the theorems ! - then i will study section 1 , 2 , 3 on chapter 5 " i read section 1 and found it easy " then turning to rings , but before the turnement to rings , i hope that we meet in the chat as we had intended . $\endgroup$
    – Fawzy Hegab
    Feb 26, 2013 at 21:09
  • $\begingroup$ i also intent to read more about Holder programme from some text - which you of course don't know ! because the writer of this text is egyptian and the text is un-known in Europe and America - it may increase my information about this great programme , in D&F , talking about Holder programme was not enough in my opinion , i guess that the details about this programme is so excitting . $\endgroup$
    – Fawzy Hegab
    Feb 26, 2013 at 21:14
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This book is very good. It covers the fundamental tools and results in set theory (Zorn's Lemma, cardinals etc.), Model theory (completeness theorem, compactness theorem), proof theory, and even touches a bit on axiomatic set theory. There are no prerequisites needed (except for some familiarity with group theory for some of the examples). It goes from the very basics to cover, rigorously and accessibly, some of the most important aspects of the theory.

I used this text several times to teach a first logic course and it was very successful.

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  • $\begingroup$ Great ! , i studied group theory from Dummit and foote , let me ask you something , after finishing finish this text which you had recommended , which text i have to study from it ? $\endgroup$
    – Fawzy Hegab
    Feb 26, 2013 at 20:37
  • $\begingroup$ that would depend on the area you'd like to deepen you understanding of. More advanced set theory, axiomatic set theory, intermediate level model theory, as well as proof theory will be accessible. $\endgroup$
    – Ittay Weiss
    Feb 26, 2013 at 20:40
  • $\begingroup$ i want to develop this knowledge to study Godel's incompleteness theorems , and of course i don't know which one of the topics you mentioned above is related with godel's theorems . $\endgroup$
    – Fawzy Hegab
    Feb 26, 2013 at 20:47
  • $\begingroup$ that would be Model Theory, and will certainly be accessible. $\endgroup$
    – Ittay Weiss
    Feb 26, 2013 at 20:56
  • $\begingroup$ Great ! thanx :) $\endgroup$
    – Fawzy Hegab
    Feb 26, 2013 at 21:15

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