6 Feb
2003
6 Feb
'03
10:44 a.m.
On Mon, 3 Feb 2003, Galchin Vasili wrote:
Hello,
I understand (to some degree) full combinatory algebra, but I don't understand the motivation behind the definition of a partial combinatory algebra. E.g. why do we have Sxy converges/is defined?
I'd like to know the answer to this too. Why does *everyone*, in writing down the definition of a PCA, include the assumption that Sxy is always defined? As far as I can see, the only answer is "because everyone else does so"; the condition is never used in the construction of realizability toposes, or in establishing any of their properties. In every case where you need to know that a particular term Sab is defined, it's easy to find a particular c such that Sabc is provably defined. Peter Johnstone