I have difficulty recommending any books on logic. Perhaps that indicates the need for the present work. Perhaps you can recommend one to me. You might want to look at:
Wilfred Hodges, Logic Penguin Books, 1977 ISBN 0140219854
The next two books on the list are definitely rather mathematical:
- Elliott Mendelson, Introduction to Mathematical Logic Wadsworth & Brooks/Cole, 1987 ISBN 0534066240
- The word 'introduction' in the title needs to be taken with a pinch of salt.
- Boolos & Jeffrey, Computability and Logic