Good books in Set theory and Mathematical Logic

In summary, the conversation discusses the search for a book on mathematical logic that only requires minimal exposure to set theory. The speaker mentions being familiar with basic set theory and mentions some recommended texts for learning mathematical logic. They also mention taking graduate level courses on the subject in the future.
  • #1
Bourbaki1123
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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.
 
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  • #2
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
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
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
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.
 

1. What is the difference between set theory and mathematical logic?

Set theory is a branch of mathematics that deals with the study of sets, which are collections of objects. It is primarily concerned with the relationships between sets and operations on sets. Mathematical logic, on the other hand, is a branch of mathematics that studies the principles of valid reasoning and argumentation. It is concerned with the study of logical systems and their applications in mathematics.

2. What are some good introductory books on set theory and mathematical logic?

Some good introductory books on set theory and mathematical logic include "A Beginner's Guide to Mathematical Logic" by Raymond Smullyan, "Set Theory: An Introduction to Independence Proofs" by Kenneth Kunen, and "An Introduction to Mathematical Logic" by Herbert Enderton.

3. Are there any specific prerequisites for studying set theory and mathematical logic?

A basic understanding of mathematical concepts such as algebra and calculus is recommended for studying set theory and mathematical logic. Familiarity with formal mathematical notation and proof techniques is also helpful.

4. Can set theory and mathematical logic be applied in other fields besides mathematics?

Yes, the principles and techniques of set theory and mathematical logic have applications in a wide range of fields, including computer science, linguistics, philosophy, and physics. They provide a foundation for studying and understanding complex systems and their properties.

5. What are some advanced books on set theory and mathematical logic?

Some advanced books on set theory and mathematical logic include "Set Theory: On the Structure of the Real Line" by Robert R. Phelps, "Axiomatic Set Theory" by Patrick Suppes, and "Model Theory: An Introduction" by David Marker. These books delve deeper into the principles and applications of set theory and mathematical logic, making them suitable for graduate level studies.

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