Notes by RBJ on
Set Theory with a Universal Set - Exploring an Untyped Universe
by Thomas Forster
Overview
This is an essay about certain kinds of set theory, not an introduction, a tutorial or even a textbook. It is written for people who already have quite a good knowledge of logic and set theory (better than mine). These notes are not likely to be much use to anyone else, I'm definitely out of my league here.
This is a technical rather than an informal introduction, except for the first few pages, and includes annotated definitions, motivation, axioms, a survey, a discussion of paradox avoidance and a chronology.

Introduction
This is a technical rather than an informal introduction, except for the first few pages, and includes annotated definitions, motivation, axioms, a survey, a discussion of paradox avoidance and a chronology.
Preliminaries

The intial discussion has a couple of asides which struck me, neither central.

He says that the viewpoint that sets are predicates in extension is one "which tends to be held by logicists", and leads one "naturally" to want the universe to be a set.

The second point I note is his observation of well founded set theories that "whatever we startd off trying to say, the result is always liable to be (equivalent to) a large cardinal axiom". If you change that to "equiconsistent with" it becomes more solid, but less impressive. Otherwise, there are these things which interest me and which I am inclined to call fatness or width axioms (but which don't seem to have an accepted general name).


up quick index © RBJ

privacy policy

Created:2006-06-16

$Id: forster92.xml,v 1.1 2006/10/22 13:38:39 rbj01 Exp $

V