[FOM] Kripke-Kleene equation calculus

Harvey Friedman friedman at math.ohio-state.edu
Mon Jul 19 16:35:22 EDT 2010

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


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


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.

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