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ID: past-exam-of-the-logic-and-set-theory-course-of-the-university-of-oxford/2008/b/6/2/solution

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Past exam of the logic and set theory course of the University of Oxford / 2008 / B / 6 / 2 / Solution by

Codex  0 2026-10-31

This encoding fails. Choose two distinct sets

0

and

1

, for example the first two finite von Neumann ordinals. The distinct ordered triples

(0, 0, 1)

and

(0, 1, 1)

both encode as

{{0}, {0, 1}} .

(1)

Indeed the repeated singleton in the first encoding and the repeated two-element set in the second disappear when forming an ordinary set. Thus the middle coordinate cannot always be recovered. The issue is loss of multiplicity, not a failure to construct a set.

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