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Results tagged with independence-results
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user 6085
This tag is for questions about proving that some statement is independent from a theory, meaning it is neither provable nor refutable from that theory. Common examples are the continuum hypothesis from the axioms of ZFC, and the axiom of choice from the axioms of ZF.
21
votes
Accepted
Is every p-point ultrafilter Ramsey?
Amit:
The converse is not true, not even under MA. This is a result of Kunen, and the paper you want to look at is "Some points in $\beta{\mathbb N}$", Math. Proc. Cambridge Philos. Soc. 80 (1976), …
- 32.5k
8
votes
Accepted
A problem about posets similar to Suslin's problem
Amit:
If ${\mathbb P}$ is a non-trivial separative partial order, and it is countable, an easy argument (back-and-forth) shows that it is forcing isomorphic to Cohen forcing. (This is an exercise in …
- 32.5k
7
votes
Statements forced by one condition of a poset, but not the whole thing
Amit: A very interesting example of non-homogeneous posets are lotteries. Joel introduced them and has done a significant amount of work on them.
Given a collection $\{{\mathbb P}_i\mid i\in I\}$ of …
- 32.5k
6
votes
Is the Axiom of Union independent of the rest of ZF?
Let me add a nice remark I just became aware of: In
Greg Oman. On the axiom of union, Arch. Math. Logic, 49 (3), (2010), 283–289. MR2609983 (2011g:03122),
Oman clarifies precisely which unions c …
- 32.5k