Decidability of P = NP

Here's an approach I thought of for to trying to show that the P vs NP
question might be undecidable. Any comments would be appreciated.

According to Baker-Gill-Solovay, there exist oracles A and B such that
P^A = NP^A and P^B != NP^B. As a result, it is concluded that P = NP
cannot be proven true or false by techniques that relativize.

Now consider a Turing machine that partially decides the language Q of
languages that are in P. By Rice's theorem, the language Q is
necessarily undecidable. However, that doesn't mean that it is
impossible for a TM to partially decide the language.

Now consider the language SAT. Assume, for the sake of contradiction,
that the TM that partially decides Q (call it R) is able to decide
whether or not SAT is in Q. If it can, then R^B, where B is the
oracle set s.t. P^B != NP^B, is also capable of deciding whether SAT
is in Q. The same holds for R^A, where A is defined as above also.

If this is true, however, then we have a proof technique that
relativizes. Running the same algorithm relative to different oracle
sets is a simple relativization of the proof technique; thus we have
found a proof that P = NP or that P != NP using a technique that
relativizes.

This contradiction shows that no TM can decide whether or not SAT is
in P, and thus no TM can decide if P = NP. Thus, either P = NP is
undecidable, or the computational model associated with the oracle
sets mentioned are inconsistent--which doesn't seem likely.

Any comments on this approach?

Thanks,
Phil
.

Relevant Pages

  • M as an implementation language
    ... M encounters the same final problems like assembler language did 30 years ... The solution was not to use assembler directly as a programming language ... even companies like oracle and MS are looking for a way out of it. ... Many M pro's use DOM's, but the theory and basics still not well founded, ...
    (comp.lang.mumps)
  • Re: Paper - impossible to prove P=?NP
    ... deterministic Turing machine with an oracle for A in polynomial time; ... The difference from "real" Turing machines is that ... Then there exists a language A for which P^A = NP^A, ... So techniques for deciding P=?NP would have to be rather deeply ...
    (sci.crypt)
  • Re: [Info-ingres] Re: What animal should Ingres be?
    ... A more 'full' language would simply allow for code more comprehensible for most of our devs. ... Some are starting to use Java so they can move their stored procs between Oracle and DB2 without translation. ... Ingres could be added to this list. ...
    (comp.databases.ingres)
  • Re: Bug tracking system recommendation
    ... run on Linux and uses either MySQL or Oracle. ... It doesn't matter too much what language it's written in, though either Java or something that doesn't require an interpreter would be preferred over Perl or PHP. ...
    (comp.lang.java.programmer)
  • Re: extracting data from a database and converting it into an XML file
    ... Because you don't really have a C or C++ LANGUAGE ... What you need is an Oracle DB library and an XML-parser library. ... Oracle and XML programming respectively. ... >> Frank Schmitt ...
    (comp.lang.cpp)