Weak saturation properties and side conditions
Abstract
Towards combining "compactness" and "hugeness" properties at $\omega_2$, we investigate the relevance of sideconditions forcing. We reduce the upper bound on the consistency strength of the weak Chang's Conjecture at $\omega_2$ using Neeman's forcing. But we find a barrier to the applicability of these methods to our problem and give a counterexample to a claim of Neeman about the effects of iterating such forcing.
 Publication:

arXiv eprints
 Pub Date:
 September 2022
 DOI:
 10.48550/arXiv.2209.00340
 arXiv:
 arXiv:2209.00340
 Bibcode:
 2022arXiv220900340E
 Keywords:

 Mathematics  Logic
 EPrint:
 Theorem 28 of the first version was false. There were some gaps in the proof of Lemma 32 and in the argument for the tree property in the last paragraph of page 24