[NOTE: These web pages are very much under construction. Much more is planned in the next 4 months or so, and some pages that are here need review and corrections or improvement. Please contact me if you have any special requests. Richard Kaye, October 2009.]
In due course I hope to have web pages containing answers or hints to all the exercises in the book. If the one you are looking for is not here yet please be patient.
The following exercises test your knowledge and understanding of the marerial in the book further. They may be suitable for assessments for undergraduate courses, etc. Answers will not normally be provided on these web pages. They may not follow the order of the book exactly.
babypropositional logic based on the arrow relation and the propositional constant bottom.
This lists some supplementary material for propositional
and first order logic, directly related to the book and available here
as additional reading, some of it advanced
. In particular
this includes the proof of the Soundness Theorem,
which is quite technical, especially
when done properly. Just like the simpler examples of Soundness
in the book, it is by induction on the length of proof. This sequence
of web pages takes the reader through the material. Along the way
you will find precise definitions of truth in an L-structure M
and the precise definitions of substitution and the rules for
first order logic. It is suitable for readers who want the full details
and who have mastered most of The Mathematics of Logic.
The Mathematics of Logic, including a way to avoid the use of Zorn's lemma and an alternative way of deriving König's lemma from the completeness theorem.
andand
or, intermediate between the systems of chapters 4 and 6 of
The Mathematics of Logic.
Possibly the most celebrated results in logic, the incompleteness theorems show there are intrinsic limitations to the idea of mechanised proof. (In other words, mathematicians are not and never will be redundant!) The pages here sketch the details and the links with computability.
Axiomatic set theory is a first order theory into which all normal
mathematics embeds. It formalises many arguments presented in The Mathematics
of Logic including results on Zorn's Lemma and cardinal numbers.
These pages build on Chapters 10 and 11 of The Mathematics of Logic. The goal is to give more examples and motivate the ideas of independence behind Morley's theorem.