Good books in Set theory and Mathematical Logic

  • #1
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Main Question or Discussion Point

I am more precisely looking for a book on mathematical logic which presupposes only minimal exposure to set theory. Preferably something which includes an introductory chapter delineating relevant set theoretic principals.

I am familiar with only basic set theory. More precisely this means that I understand the following concepts:Power sets, relations, functions, classes, union, intersection, ordered tuples. I know some group, ring and field theory.
 

Answers and Replies

  • #2
mathwonk
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as far as i know, mathematical logic, such as espoused in the book of say W.v.O.Quine, does not presuppose any set theory at all.
 
  • #3
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I don't know if Quine's book is adequate. It seems that modern mathematical logic not only requires set theory, but is built entirely upon it. This is exemplified by an example from J.D.Monk's book on the subject (I picked it up in the small library in my uni's math building):A first order language is defined to be a quadruple 'L'(fancy cursive L)= (L,v,O,R) with the following properties:
(i)L,v,O and R are functions such that RngL, Rng v(range of v), Dmn(domain)O, and Dmn R are pairwise disjoint.
(ii)DmnL=5,and L is one-one, L0 is the negation symbol of 'L',L1 is the disjunctive symbol of 'L',L2 the conjunctive symbol and L4 the equality symbol. Ect....
 
  • #4
xristy
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Since it isn't stated what the OP wants to learn of logic here are two sorts of answers.

1) To learn some of the ideas of logic in a less formal manner perhaps consider Graham Priest's "Logic: A Very Short Introduction".

2) To learn mathematical logic, then reasonable set theory texts are Lawvere "Sets for Mathematics"; and Suppes "Axiomatic Set Theory". For mathematical logic the two texts that I have found most useful are Ebbinghaus, Flum and Thomas "Mathematical Logic" (a Springer undergraduate text). The other text is a bit more advanced, J. R. Schoenfield "Mathematical Logic" more on model theory and first-order theories, not so much proof theory. Even though Schoenfield was first published in 1967 it is still quite fresh. Quine on the other hand is a bit dated.
 
  • #5
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Thanks, I decided to pick up eddinghaus already. I already know all of the material in Quine's Methods of Logic and had assumed Quine's treatment would be a bit dated. I am hopefully going to take a grad level sequence mathematical logic courses my junior and senior years. I suspect that since there is not an undergraduate course offered at the school, it will be more like an undergrad course.
 

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