Title: Forcing Construction Related to Strongly Compact Cardinals

Speaker: Liuzhen Wu (Institute of Mathematics, Chinese Academy of Sciences)

Time: 2025/04/22 (Tuesday) 15:10-18:00

Location: Room 215, Natural ​Sciences Teaching Building (理教), Peking University

Abstract:

This talk examines the relationship between forcing and large cardinal axioms, focusing on how large cardinal properties are preserved in forcing extensions and how the continuum function can be manipulated.

The first part provides an introduction to forcing and its role in the consistency proof involving large cardinals. It then discusses large cardinals, including measurable, strongly compact, and supercompact cardinals, highlighting their definitions, properties, and significance in set theory.

The second part addresses some open questions in the field, such as the connection between strongly compact cardinals and the continuum function.