| The Message Passing Interface standard, 2003. http://www-unix.mcs.anl.gov/mpi/. |
....involving AC into a contradiction involving the axioms of set theory alone. One way to handle meta level reasoning is to throw away our set theory provers and work formalistically. We could work in a weak logic, such as PRA, which has been proposed for the QED project for mechanizing mathematics [13]. In this logic, we would define the set of formulas (the set F ) an internalized inference system, and the ZF axioms. Instead of proving the theorem # in a ZF prover, we would prove the theorem ZF in PRA. Then we could easily express syntactic operations on formulas. However, the formalist ....
The QED manifesto. http://www-unix.mcs.anl.gov/qed/, 1995.
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The Message Passing Interface standard, 2003. http://www-unix.mcs.anl.gov/mpi/.
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The MPICH2 project home page, 2005. http://www-unix.mcs.anl.gov/mpi/mpich2/index.htm.
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The Message Passing Interface standard, 2003. http://www-unix.mcs.anl.gov/mpi/.
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The Globus toolkit. http://www-unix.globus.org/toolkit/, Nov. 2003.
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The Globus toolkit. http://www-unix.globus.org/toolkit/, Nov. 2003.
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