Ordinal computers

Details Ordinal computers Ordinal computers

1998-04-15

arxiv.org/abs/math/9804076v1

Mathematics

Logic

9 pages, no pictures, AMS latex

Scientific paper

Can a computer which runs for time $\omega^2$ compute more than one which
runs for time $\omega$? No. Not, at least, for the infinite computer we
describe. Our computer gets more powerful when the set of its steps gets
larger. We prove that they theory of second order arithmetic cannot be decided
by computers running to countable time.

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