[FOM] Plea for literature on recursion theory in V_\omega
csaba-ml at creo.hu
Mon Apr 28 07:36:52 EDT 2008
Dear FOM members,
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.)
Thanks for your suggestions!
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