[FOM] indepence and consistency results of set theory

Matt Insall montez at fidnet.com
Sat Apr 30 10:14:33 EDT 2005

F. A. Muller asked about literature that deals with independence results for
the axioms of set theory (other than the ``famous'' ones like AC and CH).
When I was a graduate student, I read through a little book (100 pages) by
J.L. Krivine, called ``Theorie axiomatique des ensembles'' (``Introduction
to axiomatic set theory'') (Translated into English by David Miller).  As I
recall (but I am a bit rusty on this), for some of the axioms, Krivine
presents models that can be drawn on the page (i.e. for these fragments of
set theory, there are models with a very small finite number of sets).  It
seems to me that I could ``see'' the independence of certain of the axioms
from others by looking at the figures and reading his discussion of them,
even though Krivine may not have explicitly written much about the
independences.  I never took the time to write out formal proofs of the
independence relations however.

>From a sunny day after the rain in the Missouri Ozarks.

Dr. Matt Insall
Associate Professor of Mathematics
Department of Mathematics and Statistics
University of Missouri - Rolla
Rolla MO 65409-0020

insall at umr.edu

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