One of the remarkable results of Frege＇s Logicism is Frege＇s Theorem, which holds that one can derive the main truths of Peano arithmetic from Hume＇s Principle （HP） without using Frege＇s Basic Law V. This result...One of the remarkable results of Frege＇s Logicism is Frege＇s Theorem, which holds that one can derive the main truths of Peano arithmetic from Hume＇s Principle （HP） without using Frege＇s Basic Law V. This result was rediscovered by the Neo-Fregeans and their allies. However, when applied in developing a more advanced theory of mathematics, their fundamental principles--the abstraction principles--incur some problems, e.g., that of inflation. This paper finds alternative paths for such inquiry in extensionalism and object theory.展开更多
In this paper,we show that the elliptic cocenter of the Hecke algebra of a con-nected reductive p-adic group is contained in the rigid cocenter.As applications,we prove the trace Paley-Wiener theorem and the abstract ...In this paper,we show that the elliptic cocenter of the Hecke algebra of a con-nected reductive p-adic group is contained in the rigid cocenter.As applications,we prove the trace Paley-Wiener theorem and the abstract Selberg principle for mod-l representations.展开更多
文摘One of the remarkable results of Frege＇s Logicism is Frege＇s Theorem, which holds that one can derive the main truths of Peano arithmetic from Hume＇s Principle （HP） without using Frege＇s Basic Law V. This result was rediscovered by the Neo-Fregeans and their allies. However, when applied in developing a more advanced theory of mathematics, their fundamental principles--the abstraction principles--incur some problems, e.g., that of inflation. This paper finds alternative paths for such inquiry in extensionalism and object theory.
文摘In this paper,we show that the elliptic cocenter of the Hecke algebra of a con-nected reductive p-adic group is contained in the rigid cocenter.As applications,we prove the trace Paley-Wiener theorem and the abstract Selberg principle for mod-l representations.
