A Purely Arithmetical, yet...

From: Brent Meeker <meekerdb.domain.name.hidden>
Date: Mon, 24 Aug 2009 20:52:11 -0700

Bruno, I would like to understand your arguments at a technical level,
so I started reading your March 2007 paper. But I got kinda bogged
down near the end of Section 2. Could you expand on the paragraph
that begins with "Let us define an arithmetical realisation R by a
function which assigns to each propositional letter p,q,r... an
arithmetical sentence." I understand the general idea which is to
create a mapping between propositions and arithmetical sentences
R:p->i where i is some arithmetical statement. But where do the
propositions come from? Are they the axioms appearing just above plus
the theorems that follow from them? Are there no further conditions on R?

You say that G proves A iff PA proves i(A). But doesn't that depend
on what map R is chosen? Is this a condition on R?

thnx, Brent

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Received on Mon Aug 24 2009 - 20:52:11 PDT

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