[FOM] Kripke-Kleene equation calculus

[Harvey Friedman]

In a Google search on Kripke-Kleene equation calculus, I found this:

http://dspace.mit.edu/bitstream/handle/1721.1/12166/30049830.pdf?sequence=1

referring to [13], [14], on page 11. These are

[13] G. Kreisel and G.E. Sacks, Metarecursive sets, JSL 28 (1963)   
304-305, 30 (1965)  318-338.

[14] S. Kripke, Transfinite recursions on admissible ordinals  
(abstracts), JSL 29 (1964)  161-162.

This peaked by curiosity. So a quick search turned up the educational

http://dspace.mit.edu/bitstream/handle/1721.1/33486/29976039.pdf?sequence=1

Harvey Friedman

On Jul 19, 2010, at 1:05 AM, Toby Meadows wrote:

> I am looking for some exposition of the Kripke-Kleene equation  
> calculus for transfinite recursion on admissible ordinals. I am  
> familiar with Kripke (JSL, 1964) and Kreisel/Sacks (JSL 1965), but  
> was hoping for more detailed discussion.
>
> Moreover there appear to be minor differences between the systems  
> that these authors discuss. For example, Kripke omits the successor  
> symbol, while Kreisel and Sacks retain it. Perhaps this is merely  
> cosmetic.
>
> Any assistance would be appreciated.