Is there a concise second-order logic tutorial available online?

Question

For a paper I'm writing, I need a bit of second order logic in order to convey a few steps in an inference.

I've completed the introductory and intermediate/advanced logic classes at my school (second order logic wasn't included in the curriculum, unfortunately). I use predicate logic in most of my classes, so I'm comfortable with it.

I'd like to learn just enough to properly notate the steps of the inference.

Is there a concise tutorial on the subject available online?

Answer 1

There are not a lot of formal treatments of second-order logic that will include things like annotated formal deductions. I generally view Shapiro's book Foundations without foundationalism as the most contemporary treatment of second-order logic specifically - but it is written at a higher level, and will not discuss formal proofs much.

Some general-purpose logic texts may include second-order logic in particular chapters - the fourth edition of Mendelson's book does.

Answer 2

Enderton's book has very concise introduction to second order logic at introductory level. It also has some exercises for self study. If you know some basics of deductive systems and model theory you should be able to follow.

Saphiro's "Foundations without foundationalism" book may be suitable if read partially. There is a lot of philosophy of mathematics covered by this book and I found it as a argument for second-order logic as foundation of mathematics.