TL;DR
This paper introduces a new extender-based Radin forcing that generalizes measure sequences, allowing for controlled changes in cardinal characteristics while preserving cardinals and properness.
Contribution
It develops a novel extender sequence framework that combines Gitik-Magidor and Radin forcing, enabling precise manipulation of cardinal properties.
Findings
Forcing satisfies Prikry-like condition
Preserves all cardinals during forcing
Can change cofinality and power of cardinals
Abstract
We define extender sequences, generelizing measure sequences from Radin Forcing. Using the extender sequences we combine Gitik-Magidor forcing for adding many Prikry sequences with Radin forcing. This forcing satisfies Prikry like condition, destroys no cardinals, and has a kind of properness. Depending on the large cardinal we start with, this forcing can blow the power of a cardinal together with changing its' cofinality to a prescribe value. If this prescribed value is the cardinal itself then it remains regular and even can remain measurable.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topology and Set Theory · Mathematical and Theoretical Analysis · Computability, Logic, AI Algorithms