تقرير
Increasing the second uniform indiscernible by strongly ssp forcing
| العنوان: | Increasing the second uniform indiscernible by strongly ssp forcing |
|---|---|
| المؤلفون: | De Bondt, Ben, Velickovic, Boban |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Logic, Primary: 03E35, 03E55, 03E65, Secondary: 03E05 |
| الوصف: | We introduce a new and natural stationary set preserving forcing $\mathbb P^{c-c}({\lambda},{\mu})$ that (under $\mathsf{NS}_{\omega_1}$ precipitous + existence of $H_{\theta}^#$ for a sufficiently large regular ${\theta}$) increases the second uniform indiscernible $\mathbf{u}_2$ beyond some given ordinal ${\lambda}$. The forcing $\mathbb P^{c-c}$ shares this property with forcings defined in [2] and [9]. As a main tool we use certain natural open two player games which are of independent interest, viz. the capturing games $\mathbf{G}_M^{cap}(X)$ and the catching-capturing games $\mathbf{G}_M^{c-c}(X)$. In particular, these games are used to isolate a special family of countable elementary submodels $M \prec H_{\theta}$ that occur as side conditions in $\mathbb P^{c-c}$ and thus allow to control the forcing in a strong way. Comment: Minor changes and corrections |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2212.13797 |
| رقم الأكسشن: | edsarx.2212.13797 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |