# Ralf Schindler - Talk 5 on Logic Summer School of Fudan University, 2020

Content:

• Finish the last theorem of the last lecture: Force by a stationary set preserving forcing:
$$(M;\in,I)\xrightarrow[\text{of length } \omega_1]{\text{generic iteration}}(H_{\omega_2}^V;\in,\mathbf{NS}_{\omega_1}^V),$$

where $M$ is a generically iterable countable transitive structure.

• $\Bbb P_{\max}$ forcing and analysis of $L(\Bbb R)^{\Bbb P_{\max}}$;

• $(\ast)$ and: $\mathbf{MM}^{++}\implies(\ast)$.

# Ralf Schindler - Talk 4 on Logic Summer School of Fudan University, 2020

Content:

• Show a characterization of precitiousness;
• $V$ is generically iterable with respect to precitious ideals;
• Discussion of effecitive counterexamples to $\mathbf{CH}$.
• Illustrations of Admissible Club Guessing(ACG)$\implies \mathfrak{u}_2 = \omega_2$.
• Prove ACG follows from $\mathbf{MM}$.

# Ralf Schindler - Talk 3 on Logic Summer School of Fudan University, 2020

Content:

• discuss some aspects of stationary sets;
• $\mathbf{MM}\implies 2^{\aleph_1}=\aleph_2$;
• effective counterexample to $\mathbf{CH}$.