Title: Cylindrical space and its application in first-order model theory

Speaker: Yunfei Qin (PKU)

Time: 15:10 ~ 18:00  (April. 26)

Abstract:  In daily life and study, people often use Venn's diagram as a tool for complex logical reasoning. The reason why we can use Venn's diagram to effectively deal with logical reasoning is that the reasoning relationship between logical propositions can isomorphically correspond to the inclusion relationship between sets in the set field. This correspondence can be formally described as Stone's representation theorem. Using the language of topology, stone's representation theorem can be "upgraded" to the category duality between Boolean algebra and Stone space. Under this duality, Stone space is naturally endowed with a logical semantic connotation: every point in the space can be regarded as a model of the corresponding propositional logic theory. As the development of propositional logic, by defining a kind of zero-dimensional space (especially, Stone space) with additional structure, the semantics of first-order logic can also have a set-topological representation similar to propositional logic. Further, in this report, we will also introduce how this representation can be applied as a method to deal with problems in the research of first-order model theory.