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Results tagged with set-theory
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user 14705
forcing, large cardinals, descriptive set theory, infinite combinatorics, cardinal characteristics, forcing axioms, ultrapowers, measures, reflection, pcf theory, models of set theory, axioms of set theory, independence, axiom of choice, continuum hypothesis, determinacy, Borel equivalence relations, Boolean-valued models, embeddings, orders, relations, transfinite recursion, set theory as a foundation of mathematics, the philosophy of set theory.
14
votes
How to decompose an infinite set into two isomorphic ones without choice?
No it's not, you need to have at least some choice, for example that for every set $A$ we have $|A|+|A|=|A|$. For every cardinal $\kappa$, using ZFA with $\kappa^+$ atoms, you can create a permutation …
- 331
9
votes
1
answer
856
views
$\Pi_0^1$-weakly indescribable cardinals are exactly the regulars
Hi,
I'm not sure if I should ask here or over at math.stackexchange.com, but I think here it's a bit more fitting. This question stems from a homework problem:
Definition:
Given some class of formulas …
- 331