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Year 3 of the mathematics course of the University of Oxford

Logic and set theory course of the University of Oxford

Past exam of the logic and set theory course of the University of Oxford

2011

The four principles are:

* <Axiom of choice>: for every family $(A_i)_{i\in I}$ of nonempty sets, there exists a <function> $c$ on $I$ with $c(i)\in A_i$ for all $i$.
* <Cardinal comparability principle>: for any sets $A,B$, there is an <injection> $A\hookrightarrow B$ or an <injection> $B\hookrightarrow A$.
* <Well-ordering theorem>: every set admits a <well-order>.
* <Zorn's lemma>: every nonempty <partially ordered set> in which every chain has an upper bound has a maximal element.

In the last assertion the upper bound belongs to the partially ordered set; it need not belong to the chain.

Solution

Past exam of the logic and set theory course of the University of Oxford / 2011 / B / 6 / a / Solution

Past exam of the logic and set theory course of the University of Oxford / 2011 / B / 6 / a / Solution

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