[FOM] Origins of the double turnstile

Simon Kochen kochen at math.princeton.edu
Thu Feb 2 10:57:21 EST 2017


  A use of the double turnstile that is earlier than those mentioned so 
far is In my paper "Ultraproducts in the Theory of Models",Annals of 
Mathematics, v.74,1961,pp221-261, where I define and makes extensive 
use  of it. The paper is based on my 1959 Ph.D. thesis in Princeton, 
which also uses the double turnstile. I cannot  recollect whether I 
originated it or took it from some other paper.

Simon Kochen

On 1/6/2017 12:47 PM, Christopher Menzel wrote:
> FOM folk,
> The turnstile (\vdash) is typically traced back to Frege and was picked up by Whitehead and Russell, who used it more or less to indicate provability, and of course this largely continues to the present day. But whence the double turnstile (\models) to indicate logical consequence? I thought perhaps I'd find it in Carnap or, at least, in Kemeny's famous 1956 JSL articles, but it's not there; they just adopt ordinary language expressions to indicate semantic relations. From the very limited bit of searching I've done, the double turnstile appears to be of fairly recent vintage. Does anyone know its origins or, at least, can anyone point to an earlyish (even pre-1960) use of the notation?
> Thanks.
> Chris Menzel
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