[FOM] Uniformly Reflexive Structures (URS)

[David Leduc]

Thank you very much for the reference. I have no doubt it is a great work
since you recommended it. However it is not what I expected.

In the introduction of the first paper by Wagner on URS it is written: "we
want to develop our axiomatic structure on a sufficiently abstract level so
that [...] it does not depend [...] on special specific functions." But
then two of the three axioms are stating the existence of special specific
functions alpha and psi! Well, it looks to me like yet another
Turing-complete programming language although this time it is disguised as
an axiomatic system.

D.




On Tue, Apr 16, 2013 at 8:39 PM, Harvey Friedman <hmflogic at gmail.com> wrote:

> From http://www.cs.nyu.edu/pipermail/fom/2013-April/017210.html
>
> >I have a question about computability. I am sure it is well known but
> >I cannot find the answer in my textbooks.
> >
> >For any system that is Turing complete, one can define a universal
> >machine in this system.
> >
> >But I want to do thing the other way round. Assume a system that has a
> >universal machine as one of its primitive instructions. What are the
> >other primitives needed to make this system Turing-complete?
>
> You may want to look at the URS. These are the uniformly reflexive
> structures of Wagner and Strong,and also Strong's BRFT. This stuff is
> not sufficiently studied in recent years.
>
> http://www.ams.org/journals/tran/1969-144-00/S0002-9947-1969-0249297-9/
>
> http://domino.research.ibm.com/tchjr/journalindex.nsf/4ac37cf0bdc4dd6a85256547004d47e1/efac077da47cb91685256bfa00683ffe!OpenDocument
>
> Harvey Friedman
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