For an uncountable cardinal $ \kappa$ , we are interested in the least size of a cofinal subset of the partial order $ ([\kappa]^\omega, \subseteq)$ . It is obvious that this cofinality is at least $ \kappa$ and a rather simple induction shows that $ cof([\aleph_n]^\omega, \subseteq)=\aleph_n$ for each natural number $ n \geq 1$ .
What is known in $ ZFC$ for bigger cardinals?
Also I am intrigued by the following statement made by Alan Dow in Efimov spaces and the splitting number, Topology Proc. (2005):
It is a “large cardinal” hypothesis to assume that there is a cardinal $ \kappa$ with uncountable cofinality such that this cofinality is greater than $ \kappa$ .
What exactly does he mean by that, and what is a good reference to read about it?
✓ Extra quality
ExtraProxies brings the best proxy quality for you with our private and reliable proxies
✓ Extra anonymity
Top level of anonymity and 100% safe proxies – this is what you get with every proxy package
✓ Extra speed
1,ooo mb/s proxy servers speed – we are way better than others – just enjoy our proxies!
Our proxies have TOP level of anonymity + Elite quality, so you are always safe and secure with your proxies
Use your proxies as much as you want – we have no limits for data transfer and bandwidth, unlimited usage!
Superb fast proxy servers with 1,000 mb/s speed – sit back and enjoy your lightning fast private proxies!
99,9% servers uptime
Alive and working proxies all the time – we are taking care of our servers so you can use them without any problems
No usage restrictions
You have freedom to use your proxies with every software, browser or website you want without restrictions
Perfect for SEO
We are 100% friendly with all SEO tasks as well as internet marketing – feel the power with our proxies
Buy more proxies and get better price – we offer various proxy packages with great deals and discounts
We are working 24/7 to bring the best proxy experience for you – we are glad to help and assist you!