We discuss the past and future of set theory, axiom systems and independence
results. We deal in particular with cardinal arithmetic

A. Blass

A. Levy

A. Villaveces For Many

C. Laskowski

G. Cherlin

I Thank J. Baldwin

J. Kennedy

J. Väänänen

P. Eklof

Saharon Shelah

U. Hrushovski

English

arXiv

Abstract. We discuss the past and future of set theory, axiom systems and independence results. We deal in particular with cardinal arithmetic. Reading instructions: The real instructions, i.e., my hopes, are that you start at the beginning and read until the end. But if you are looking for advice on how much not to read and still get what you like, note that the sections are essentially independent. If you wonder what the relevance of mathematical logic is to the rest of mathematics and whether you implicitly accept the usual axioms of set theory (that is, the axioms of E. Zermelo and A. Fraenkel with the Axiom of Choice, from nowonreferredtoasZFC),youshouldreadmainly§1. If you are excited about the independence phenomenon, you should read §2. If you are interested in considerations on new additional axioms and/or in looking at definable sets of reals (as in descriptive set theory) as compared to general sets of reals, and in looking more deeply into independence, you should go to §3. For more on independence in set theory, see §4. If you really are interested in cardinal arithmetic, i.e., the arithmetic of infinite numbers of G. Cantor, go to §5. I had intended to also write sections on “Pure model theory”, “Applied model theory”, and “On Speculations and Nonsense”, but only §6 materialized

CiteSeerX

LOGICAL DREAMS

Logical Dreams

Logical Dreams

Abstract

Similar works

Full text

Available Versions

CiteSeerX