ONT Re: Remodeling Model Theory
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John Collier wrote (JC):
Jon Awbrey wrote (JA):
Jerry ??? wrote (J?):
J?: The quote from the 1973 reference is OK as far as it goes.
Modern Model Theory starts from somewhat different premises.
Recall that 1973 is ancient history in so far as model theory
or category theory are concerned.
J?: If you wish to start from a more current reference, it may lead to a more
efficient discussion of current state of affairs between logic and science.
JA: Recherché Ironic Pose (RIP) # 47.
[pleonasm deleted]
JC: It is still the first thing I would send someone to who had a math logic
background (not logic background) and wanted to know model theory.
Jefferey's 'Formal Logic: Its Scope and Limits' is quite enough
for most purposes in logic. I can't recall any significant
differences where the two overlap. Kalish and Montague:
'Deductive Logic' is an alternative to Jeffrey. Then
there are literally hundreds of derivative works.
I don't know of any more recent definitive source
at the elementary level. Barwise and Seligman,
'Information Theory', use a lot of stuff not
in C&K, but I don't think they use anything
not definable within the scope of even the
other two sources I mention, insamuch as
used concepts are definable. The only
caveat is 2-order concepts, which aren't
strictly definable in any case. Gila Sher,
'The Bounds of Logic', gives an excellent account
of the semantic and syntactic bounds of mathematics
and logic, and how they compare. I recommend it to
anyone puzzled by how the recent discussions have gone.
She takes both the position that mathematics and logic are
one study (logicism, associated with Russell, and versions of
intuitionism associated with Penelope Maddy and Verena Huber Dyson,
among others), and that they are not (constructivist intuitionism,
associated with von Neumann, among others), and looks at their merits
and problems.
I am currently looking at:
| Bruno Poizat,
|'A Course in Model Theory',
| Translated by Moses Klein,
| Springer, New York, NY, 2000.
It is refreshingly strange.
Here is a bibliography that I started compiling for the SUO WG:
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Bibliography on Logical Formalization & Mechanization
| Barwise, Jon & Etchemendy, John,
|'The Language of First-Order Logic',
| Including the Program 'Tarski's World',
| CSLI Lecture Notes, Number 23,
| CSLI, Stanford, CA, 1990.
| Bell, John L. & Machover, Moshé,
|'A Course in Mathematical Logic',
| North-Holland, Amsterdam, Netherlands, 1977.
| Chang, Chin-Liang & Lee, Richard Char-Tung,
|'Symbolic Logic and Mechanical Theorem Proving',
| Academic Press, New York, NY, 1973.
| Crossley, J.N., et al.,
|'What Is Mathematical Logic',
| Oxford University Press, Oxford UK, 1972.
| van Dalen, Dirk,
|'Logic and Structure', Second Edition,
| Springer-Verlag, Berlin, Germany, 1983.
| Dijkstra, Edsger W. & Scholten, Carel S.,
|'Predicate Calculus and Program Semantics',
| Springer-Verlag, New York, NY, 1990.
| Ebbinghaus, H.-D., Flum, J., & Thomas, W.,
|'Mathematical Logic',
| Springer-Verlag, New York, NY, 1984.
| Gries, David & Schneider, Fred B.,
|'A Logical Approach to Discrete Math',
| Springer-Verlag, New York, NY, 1993.
| Hilbert, David & Ackermann, Wilhelm,
|'Principles of Mathematical Logic',
| Chelsea Publishing, New York, NY, 1950.
| Jeffrey, Richard,
|'Formal Logic: Its Scope and Limits',
| Second Edition, McGraw-Hill, New York, NY, 1981.
| Kowalski, Robert,
|'Logic for Problem Solving',
| North-Holland, New York, NY, 1979.
| Lloyd, John Wylie,
|'Foundations of Logic Programming',
| Springer-Verlag, Berlin, Germany, 1984.
| Quine, W.V.,
|'Methods of Logic', Fourth Edition,
| Harvard University Press, Cambridge, MA, 1982.
| Robinson, J.A.,
|'Logic: Form and Function;
| The Mechanization of Deductive Reasoning',
| Elsevier North Holland, New York, NY, 1979.
| Smullyan, Raymond M.,
|'First-Order Logic',
| Dover Publications, Mineola, NY, 1995.
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