Corpus ID: 53127255

The fine structure of operator mice

@article{Schlutzenberg2016TheFS,
  title={The fine structure of operator mice},
  author={Farmer Schlutzenberg and Nam Trang},
  journal={arXiv: Logic},
  year={2016}
}
We develop the theory of abstract fine structural operators and operator-premice. We identify properties, which we require of operator-premice and operators, which ensure that certain basic facts about standard premice generalize. We define fine condensation for operators $\mathcal{F}$ and show that fine condensation and iterability together ensure that $\mathcal{F}$-mice have the fundamental fine structural properties including universality and solidity of the standard parameter. 
A premouse inheriting strong cardinals from V
TLDR
It is proved that a slight weakening of $(k+1)$-condensation follows from $(k,\omega_1 +1)-iterability in place of ($k, \omega-1,\omg1-1) -iterability) and that full $(k-2)-condensing follows from ($k-3)-solidity; these facts are needed in the proofs of the results above. Expand
Determinacy from strong compactness of ω 1 1 Nam Trang
4 In the absence of the Axiom of Choice, the “small” cardinal ω1 can exhibit prop5 erties more usually associated with large cardinals, such as strong compactness and 6 supercompactness. For a localExpand
Determinacy from strong compactness of $\omega_1$
In the absence of the Axiom of Choice, the "small" cardinal $\omega_1$ can exhibit properties more usually associated with large cardinals, such as strong compactness and supercompactness. For aExpand
A brief account of recent developments in inner model theory
The goal of this survey paper is to give an overview of recent developments in inner model theory. We discuss several most important questions in the field and relevant work (partially) answeringExpand
Ideals and Strong Axioms of Determinacy
Θ is the least ordinal α with the property that there is no surjection f : R → α. ADR is the Axiom of Determinacy for games played on the reals. It asserts that every game of length ω of perfectExpand
The definability of the extender sequence $\mathbb{E}$ from $\mathbb{E}{\upharpoonright}\aleph_1$ in $L[\mathbb{E}]$.
Let $M$ be an iterable fine structural mouse. We prove that if $E\in M$ and $M\models$``$E$ is a countably complete short extender whose support is a cardinal $\theta$ andExpand

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