[Inquiry] Model Theory Unplugged

[Jon Awbrey]

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MTU.  Note 1

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I want to try and say a few things about the grounds out of which the
subject that we now know under various names as "formal semantics" or
"model theory" arose, long before it became "formal" or started to be
regarded as a "theory" in its own right.

Properly viewed, model theory is just a systematic
body of techniques for generating concrete examples
of abstract theories.  Most theories are "abstract"
in some sense or other, but "concrete" is a very
relative term.

In essence, a "model" is anything about which a theory is true.
At their simplest, theories can be single sentences, or even
single signs.  At their simplest, then, models are just the
"denotations" of expressions or the "objects" of signs.

Viewed this way, a lot of what we now call formal semantics or
model theory becomes continuous, as it was in the beginning,
with the rest of what goes on in logic and mathematics.

Another thing that one can see from this longer view is that
there are natural models, the things in nature about which
theories are true, and there are artificial models, the
kinds of constructions that we are able to build out
of primitive formal materials, and about which we
also say that theories are true.  If there is
a flaw in formal model theory as it is often
presented today, it is that it does not
sufficiently stress and reinforce this
connection between artificial models
and natural models, a thing that was
one of the sources of motivation for
creating the subject in the first
place, and that remains one of
the best reasons for troubling
oneself to learn it today.

So I will try to present model theory in that light.

This point of view is easily connected up with all
of the fol-de-rol that one finds in contemporary
textbooks, a linkage to which I include once
again below, whenever we get up to that.

Jon Awbrey

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MOD.  Model Theory

1.  Introduction

1.1.  What Is Model Theory?

01.  http://suo.ieee.org/ontology/msg03985.html
02.  http://suo.ieee.org/ontology/msg03986.html
03.  http://suo.ieee.org/ontology/msg03987.html

1.2.  Model Theory for Sentential Logic

04.  http://suo.ieee.org/ontology/msg03988.html
05.  http://suo.ieee.org/ontology/msg03989.html
06.  http://suo.ieee.org/ontology/msg03991.html
07.  http://suo.ieee.org/ontology/msg03992.html
08.  http://suo.ieee.org/ontology/msg03993.html
09.  http://suo.ieee.org/ontology/msg03994.html
10.  http://suo.ieee.org/ontology/msg03995.html
11.  http://suo.ieee.org/ontology/msg03996.html
12.  http://suo.ieee.org/ontology/msg03997.html
13.  http://suo.ieee.org/ontology/msg03999.html
14.  http://suo.ieee.org/ontology/msg04000.html
15.  http://suo.ieee.org/ontology/msg04001.html
16.  http://suo.ieee.org/ontology/msg04002.html
17.  http://suo.ieee.org/ontology/msg04003.html
18.  http://suo.ieee.org/ontology/msg04004.html

1.3.  Languages, Models, and Satisfaction

19.  http://suo.ieee.org/ontology/msg04005.html
20.  http://suo.ieee.org/ontology/msg04006.html
21.  http://suo.ieee.org/ontology/msg04007.html
22.  http://suo.ieee.org/ontology/msg04008.html
23.  http://suo.ieee.org/ontology/msg04009.html
24.  http://suo.ieee.org/ontology/msg04010.html
25.  http://suo.ieee.org/ontology/msg04011.html
26.  http://suo.ieee.org/ontology/msg04012.html
27.  http://suo.ieee.org/ontology/msg04016.html
28.  http://suo.ieee.org/ontology/msg04017.html
29.  http://suo.ieee.org/ontology/msg04019.html
30.  http://suo.ieee.org/ontology/msg04020.html
31.  http://suo.ieee.org/ontology/msg04021.html

1.4.  Theories and Examples of Theories

32.  http://suo.ieee.org/ontology/msg04022.html
33.  http://suo.ieee.org/ontology/msg04023.html
34.  http://suo.ieee.org/ontology/msg04024.html
35.  http://suo.ieee.org/ontology/msg04025.html
36.  http://suo.ieee.org/ontology/msg04026.html
37.  http://suo.ieee.org/ontology/msg04027.html
38.  http://suo.ieee.org/ontology/msg04028.html

1.5.  Elimination of Quantifiers

39.  http://suo.ieee.org/ontology/msg04029.html
...

The above material is excerpted from:

| C.C. Chang and H.J. Keisler, 'Model Theory',
| North-Holland, Amsterdam, Netherlands, 1973.

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