On 13/04/2013 7:10 PM, Jesse F. Hughes wrote: > Nam Nguyen <firstname.lastname@example.org> writes: > >> On 13/04/2013 3:18 PM, Peter Percival wrote: >>> Nam Nguyen wrote: >> >>> >>> No, I know of more than one signature for PA (and I wouldn't be >>> surprised if there are others) so I'm asking you which of them you are >>> using. >>> >>>> Now that you understand which of L(S,+,x,0) and L(<,S,+,x,0) >>> >>> I don't know. >> >> OK. Let's cut the chase then: For L(PA) I've used what Shoenfield used, >> which is L(<,S,+,x,0). > > I wonder why the heck you couldn't have said that several posts ago.
You should not have wondered why the heck that was the case because:
(a) iirc, for 10+ years around here, typical posters like Torkel Franzen, Chris Menzel, Franz Fritsche, Aatu Koskensilta, George Greene, Jesse F. Hughes, etc.. have not have to spell out all the symbols of L(PA), all the axioms of PA, when they mentioned _the familiar_ "L(PA)" or "PA" and there was no need to spell them out.
Why should I do anything different from what typical posters have done in this respect.
(b) What is the need for anyone to know exactly what the signature of _the familiar_ L(PA) that one has to bother asking people? What's the difference in this context? Would a choice between 2 versions of L(PA) that needs to be taken for granted hurt any argument in this context?
(c) I could have suggested to them to read standard textbooks and choose at will which signature choice they'd prefer: in this context it does _NOT_ matter what choice; and so one doesn't have to be bothered with.
Now that that has been spelled out, however unnecessarily, what's next?
Can you or they give me a straightforward statement of understanding or not understanding of Def-1, Def-2, F, F' I've requested?
-- ---------------------------------------------------- There is no remainder in the mathematics of infinity.