Hilbert's Early Metatheory Revisited

重访希尔伯特的早期元理论

阅读:1

Abstract

The article offers a novel reconstruction of Hilbert's early metatheory of formal axiomatics. His foundational work from the turn of the last century is often regarded as a central contribution to a "model-theoretic" viewpoint in modern logic and mathematics. The article will re-assess Hilbert's role in the development of model theory by focusing on two aspects of his contributions to the axiomatic foundations of geometry and analysis. First, we examine Hilbert's conception of mathematical theories and their interpretations; in particular, we argue that his early semantic views can be understood in terms of a notion of translational isomorphism between models of an axiomatic theory. Second, we offer a logical reconstruction of his consistency and independence results in geometry in terms of the notion of interpretability between theories.

特别声明

1、本页面内容包含部分的内容是基于公开信息的合理引用;引用内容仅为补充信息,不代表本站立场。

2、若认为本页面引用内容涉及侵权,请及时与本站联系,我们将第一时间处理。

3、其他媒体/个人如需使用本页面原创内容,需注明“来源:[生知库]”并获得授权;使用引用内容的,需自行联系原作者获得许可。

4、投稿及合作请联系:info@biocloudy.com。