The fine structure of operator mice
Abstract
We develop the fine structure theory of operator-premice. These are a generalization of standard premice, in which an abstract operator is used to form the successor steps in the internal hierarchy of the premouse, instead of Jensen's -operator (which computes rudimentary closure). Such notions have seen applications in core model induction arguments, but their theory has not previously been developed in detail. We define fine condensation for operators and show that fine condensation and iterability together ensure that -mice have the fundamental fine structural properties including universality and solidity of the standard parameter.
Keywords
Cite
@article{arxiv.1604.00083,
title = {The fine structure of operator mice},
author = {Farmer Schlutzenberg and Nam Trang},
journal= {arXiv preprint arXiv:1604.00083},
year = {2025}
}
Comments
69 pages. Major expository improvements. Some def's removed (without change in math). Changes in proof of solidity (3.45): added more details, esp. Claim 3.45.7, and in dealing with superstrong extenders (esp. p.59, when $E^V_{\eta'}$ superstrong, and Claim 3.45.5). Replaced k-simple DJ with standard weak DJ. Simplified copying of iteration trees. Other minor mathematical changes and corrections