Computability Theory and Its Applications

该奖项是根据2009年《美国复苏和再投资法案》(公法111-5)提供资金的。在这个项目中，Antonio Montalban研究纯可计算性理论和应用可计算性理论中的问题。纯可计算性理论中的问题是正在进行的了解图灵度结构的计划的一部分。至于应用可计算性理论，蒙塔尔班运用可计算性理论的方法，研究古典数学和数学基础各个领域的有效内容和证明理论的力量。他专注于与线性排序、布尔代数和序数有关的问题，但不是唯一的问题。可计算性理论是研究算法概念的逻辑领域。它的应用基于这样一种理念，即可以用算法解决的问题比不能用算法解决的问题简单。它用于各种方式来衡量数学对象、结构和证明的复杂性。通常情况下，这种分析可以更好地理解所研究的主题。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). In this project, Antonio Montalban studies problems in both pure and applied Computability Theory. The problems in pure computability theory are part of the ongoing program to understand the structure of the Turing Degrees. As for applied computability theory, Montalban applies methods from computability theory to study the effective content and proof-theoretical strength of various areas of both classical mathematics and foundations of mathematics. He concentrates in problems related to linear orderings, Boolean algebras, and ordinals, but not exclusively. Computability Theory is the area of Logic that studies the notion of algorithm. Its applications are based on the idea that problems that can be solved using algorithms are simpler than the ones that cannot. This is used in various ways to measure the complexity of mathematical objects, constructions and proofs. It is usually the case that this analysis gives a better understanding of the subject under study.