Davis's honor roll

Richard Zach rzach at ucalgary.ca
Thu Jun 24 10:36:52 EDT 2021

At https://cs.nyu.edu/pipermail/fom/2003-May/006665.html Martin Davis 

> I'm fond of noting that the list of logicians who have seriously proposed
> formal systems that turned out to be inconsistent reads like an honor roll:
> Frege, Church, Curry, Quine, Rosser.
I wrote up that list (with some additions) the other day


and then Panu Raatikainen reminded me of Martin's post.

My question is: which theory of Rosser's proved to be inconsistent and 
who showed it inconsistent?

Are there other examples? (I already have Russell's substitutional 
theory, Kreisel's theory of constructions, and the 1971 version of 
Martin-Löf type theory.)

There was some discussion of whether Reinhardt belongs on the list, ie, 
whether the existence of a Reinhardt cardinal was proposed as an axiom 
rather than merely put forward as a question -- perhaps someone who has 
access to Reinhardt's thesis can clarify -- or someone who was there at 
the time like Bob Solovay!?

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