Re: Equivalent to Axiom of Choice?

Theorem: Every partially ordered set can be extended to a total order.

it does not even imply that every Boolean algebra has a prime ideal.

How about the following kind-of-dual variant - where does it fit into
the one-way implications above:


### Every partial order can be RESTRICTED to a maximal total order.


"Maximal" here refers to order-preserving inclusions.

Bill Taylor

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