<logic> An attempt to avoid both relativity and vicious circularity in the proof of the consistency of formal systems of arithmetic, by using only a small set of extremely intuitive operations to prove the consistency of the system containing that set. (A second phase of the program was to build all of mathematics on the system thus certified to be consistent.) Hopes of accomplishing Hilbert's program were dashed by Goedel's second incompleteness theorem.
See Goedel's theorems, relative consistency proof
[Glossary of First-Order Logic]
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