All Questions
Tagged with order-theory forcing
6 questions
8
votes
4
answers
630
views
closure of separative quotients
Does there exist a partial order, nontrivial for forcing, that is countably closed, but whose separative quotient is not countably closed? Supposing the answer is yes, then is there a partial order, ...
5
votes
1
answer
356
views
Calculate the $\downarrow$, $\downarrow\uparrow$ and $\uparrow\downarrow$ cofinalities of the poset of nontrivial finitary partitions of $\omega$
Let $(P,\le)$ be a poset. For a point $x\in P$ let
$${\downarrow}x=\{p\in P:p\le x\}\quad\text{and}\quad{\uparrow}x=\{p\in P:x\le p\}$$be the lower and upper sets of the point $x$, and for a subset $...
3
votes
2
answers
432
views
When is a filter generated by a (countable) chain?
In any partial order $(P,\leq)$ it is easy to see that every chain generates (i.e., by taking the upwards closure) a filter, and any filter built as a result of the Rasiowa-Sikorski lemma in forcing ...
4
votes
3
answers
395
views
Problem understanding a passage of the proof of $\mathfrak{p}=\mathfrak{t}$ involving forcing
I've a problem with a passage of the proof of Claim 14.7 of the paper "Cofinality spectrum theorems in model theory, set theory, and general topolgy" by Malliaris and Shelah, or equivalently ...
11
votes
2
answers
682
views
On Applications of Forcing in Domain Theory
An interesting feature of domain theory is to use partial orders in order to provide a mathematical model for the computational approximation in a potentially infinite computational process (e.g. ...
3
votes
2
answers
689
views
A problem about posets similar to Suslin's problem
Suslin's problem is:
Given a complete dense linear order without endpoints, if it has the ccc must it be isomorphic to $\mathbb{R}$?
The answer is that it's independent of ZFC. The related ...