[FOM] Historical notation question

giovanni sambin sambin at math.unipd.it
Tue Feb 24 15:59:24 EST 2004

>I've been wondering this for a while, and since someone else just
>asked me, I though I'd ask here. Does anyone know the origin of the notation
>\Sigma_i and \Pi_i for the different levels of the arithmetic
>Brian Postow

Sigma is a common notation for disjoint unions and similarly Pi is 
the common notation for direct products. In the proposition-as-sets 
interpretation, disjoint unions and direct products are just the same 
thing as existential and universal quantification, respectively (the 
standard reference here is Martin-Loef's type theory). This is a 
justification by content, and not a proper historical reconstruction 
of the origin. But perhaps the two are connected.

Giovanni Sambin

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