So I have been learning Hilbert style FOL from "Introduction to Mathematical Logic" but some people say that it is impractical. On the other hand , I want to study axiomatic set theory , real-analysis etc using a FOL deductive system. So I have been trying to learn Fitch-style Natural Deduction for Propositional and Predicate Calculus.
The textbook I am trying to find should have the following things:
(1)FOL syntax.
(2)A logical deductive system (Natural Deduction fitch style).
(3)Conventional and self contained.
(4)Should be Concise.
(5)Only requires pen and paper.
I have found one book "Language, Proof and Logic" but I found it a bit too wordy for It has a lot of exercises which requires the programmes provided with the paid version of the book.I have the free version,So I might miss out on a lot of things I could have learned.I haven't been able to find any other book about this subject.Does anyone know of a textbook where I can learn this kind of Deductive system to use for all mathematics?
forall x checks all the points in your list. It doesn't discuss examples from concrete mathematical theories, but it introduces the formalism generally enough to be applicable to set theory and the like, and is well-written i.m.o., and completely free.