Ideals, forcing, inner models, and set theory of the reals

There are realists and there are idealists, amirite?

Since Solovay’s model, we have a pretty good idea of how ideals, forcing, and inner models interact with the set theory of the reals, especially in the study of regularity properties. I’ve been particularly drawn to the idealized forcing approach. I even tweeted about it once upon a time.

References

2026

arXiv Preprint

Ideals, Well-Orderable Families, and Baire Category in Truss’s Feferman-Type Model

Jason Zesheng Chen

2026

Bib HTML PDF

@misc{chenIdealsWellOrderable2026,
  title = {Ideals, Well-Orderable Families, and Baire Category in Truss's Feferman-Type Model},
  author = {Chen, Jason Zesheng},
  year = {2026},
  publisher = {arXiv},
  doi = {10.48550/arXiv.2608.21649},
  keywords = {FOS: Mathematics,Logic (math.LO)}
}