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arXiv · 2209.10247

Iterated club shooting and the stationary-logic constructible model

Ur Ya'ar
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Abstract

We investigate iterating the construction of $C(\mathtt{aa})$, the $L$-like inner model constructed using stationary-logic. We show that it is possible to force over generic extensions of $L$ to obtain a model of $V=C(\mathtt{aa})$, and to obtain models in which the sequence of iterated $C(\mathtt{aa})$s is decreasing of arbitrarily large order types. For this we prove distributivity and stationary-set preservation properties for countable iterations of club-shooting forcings using mutually stationary sets, and introduce the notion of mutually fat sets which yields better distributivity results even for uncountable iterations.

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Ur Ya'ar. 2022-09-21. Iterated club shooting and the stationary-logic constructible model. https://doi.org/10.1142/s0219061325500229

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