Mathematical Sciences: Bounded Computation

霍特将继续研究由图灵可计算性增强引起的度结构。这些增强是通过在图灵计算的各个方面设置尺寸限制来获得的。她尤其对真值表的可约性、弱真值表的可约性和多项式时间有界图灵可约性感兴趣。她计划开发解决学位结构问题的技术方法，并从适合于学位结构的证明技术方面对学位结构进行分析。通过这种方式，她希望揭示各种学位结构之间迄今为止隐藏的联系。该项目的其他方面是继续Haught在逆向数学背景下对模型论和递归论之间相互作用的研究，以及对可约集性质的研究，但主要的努力将投入到理解命题不可证明的意义上。利用上面提到的各种理想化的可计算性。

Haught will continue her investigation of the degree structures induced by strengthenings of Turing computability. These strengthenings are obtained by placing size restrictions on various aspects of a Turing calculation. In particular, she is interested in truth table reducibility, weak truth table reducibility, and polynomial-time bounded Turing reducibility. She plans to develop technical methods for solving structural questions about the degrees, and to analyze the degree structures in terms of the proof techniques which are appropriate to the structures. In this way she hopes to uncover heretofore hidden connections among the various degree structures. Other aspects of the project are a continuation of Haught's study of the interactions between model theory and recursion theory in the setting of reverse mathematics, and an investigation of the properties of introreducible sets, but the major effort will be invested in understanding what it means for a proposition to be unprovable, making use of the various idealizations of computability cited above.