# [FOM] Plea for literature on recursion theory in V_\omega

Jesse Alama alama at stanford.edu
Wed Apr 30 12:05:33 EDT 2008

Csaba Henk <csaba-ml at creo.hu> writes:

> I am to write my PhD thesis. I plan to base my "design" on recursion
> theory built up in V_\omega (ie., the universe of hereditarily finite
> sets [as a first-order structure with the language of set theory]).
>
> All textbooks I know of use an arithmetic context for explaining
> recursion theory. I'd like to ask: do you know of some book which uses
> V_\omega for this purpose? Or any book which discusses the well-known
> semantic equivalence (yes, this is a vague term, but you should know
> what I mean...) of <\omega, + , *> and <V_\omega, \epsilon> ?
>
> (I know this is a well explored area, but I don't know how much of this
> remained "folklore"... My focus is on finding nicely worded definitions
> and theorems which I can use as references for my original work.)
>

You may want to look at S. Swierczkowski's _Finite Sets and Gödel's
Incompleteness Theorems_, in the Dissertationes Mathematicae series
(#422).  You might be able to download a PDF copy from the DM website.

Jesse

--
Jesse Alama (alama at stanford.edu)