[FOM] Vaught - some new work.
John Baldwin
jbaldwin at uic.edu
Mon Mar 11 11:09:55 EDT 2013
Thanks first to the several people who provided me with copies of the
Vaught paper. I asked for this because I had a bad conscience about a
remark he made in that paper taking a very restrictive (from my
standpoint) of the meaning of `syntax' (footnote 35 of 2).
My two papers
1) Formalization, Primitive Concepts and Purity
and 2) Completeness and Categoricity (in power): Formalization without
Foundationalism
at http://homepages.math.uic.edu/~jbaldwin/model11.html
exhibit somewhat different views about the role of formalism in
mathematics. The first expresses some limitations of formal methods in
dealing with the concept of
purity and develops some aspects of Juliette Kennedy's notion of formalism
freeness.
The second builds off questions of Detlefsen about the `virtue' of notions
such as categoricity and completeness. It argues that formal methods and
in particular the notion of classifying first order theories by
`essentially syntactic' properties is an important tool in
mathematics and should be recognized by philosophers as a fundamental use
of formal methods.
VAUGHT. There are two Vaught papers. 1959 - `Denumerable models of
Complete Theories',* Infinitistic Methods, Proc. Symp. Foundations of
Math*. This is hard to get.
VAUGHT'S 59 paper IS POSTED AS A REFERENCE BETWEEN THE 6TH AND 7TH ITEM ON
the same webpage http://homepages.math.uic.edu/~jbaldwin/model11.html
In 1961, Vaught published in the Bulletin of the AMS, `Models of Complete
Theories'. This is more a summary of the area with few proofs and not
including proof of such results
and no complete theory with two countable models and the Vaught 2-cardinal
theorem (which are in the first paper).
It is readily available on project Euclid.
(The appendix to Formalism freeneess... by Bill Howard and myself
provides a fully geometric proof entirely
in the projective case that a Desarguesian projective plane can be imbedded
in 3 space)
Finally my great thanks to the many people who responded with copies of
Vaught's paper.
--
John T. Baldwin
Professor Emeritus
Department of Mathematics, Statistics,
and Computer Science M/C 249
jbaldwin at uic.edu
851 S. Morgan
Chicago IL
60607
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