Fwd: Davis's honor roll

[Ruy Jose Guerra Barretto de Queiroz]

---------- Forwarded message ---------
De: Richard Zach <rz...@ucalgary.ca>
Date: qui., 24 de jun. de 2021 às 17:43
Subject: Davis's honor roll
To: f...@cs.nyu.edu <f...@cs.nyu.edu>

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

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

https://richardzach.org/2021/06/23/famous-logicians-and-their-inconsistent-theories/

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!?

-Richard