Graduate studies at Western
|Abstract||We develop fundamental aspects of the theory of metric, Hilbert, and Banach spaces in the context of subsystems of second-order arithmetic. In particular, we explore issues having to do with distances, closed subsets and subspaces, closures, bases, norms, and projections. We pay close attention to variations that arise when formalizing deﬁnitions and theorems, and study the relationships between them. For example, we show that a natural formalization of the mean ergodic theorem can be proved in ACA0; but even recognizing the theorem’s “equivalent” existence assertions as such can also require the full strength of ACA0.|
|Keywords||No keywords specified (fix it)|
No categories specified
(categorize this paper)
|Through your library||Only published papers are available at libraries|
Similar books and articles
Jeremy Avigad (2000). Interpreting Classical Theories in Constructive Ones. Journal of Symbolic Logic 65 (4):1785-1812.
C. Ward Henson, Matt Kaufmann & H. Jerome Keisler (1984). The Strength of Nonstandard Methods in Arithmetic. Journal of Symbolic Logic 49 (4):1039-1058.
Carl Mummert & Stephen G. Simpson (2005). Reverse Mathematics and Π21 Comprehension. Bulletin of Symbolic Logic 11 (4):526-533.
H. Jerome Keisler (2006). Nonstandard Arithmetic and Reverse Mathematics. Bulletin of Symbolic Logic 12 (1):100-125.
Ksenija Simic (2007). The Pointwise Ergodic Theorem in Subsystems of Second-Order Arithmetic. Journal of Symbolic Logic 72 (1):45 - 66.
Ulrich Kohlenbach (1999). A Note on Goodman's Theorem. Studia Logica 63 (1):1-5.
Douglas K. Brown & Stephen G. Simpson (1993). The Baire Category Theorem in Weak Subsystems of Second-Order Arithmetic. Journal of Symbolic Logic 58 (2):557-578.
Sorry, there are not enough data points to plot this chart.
Added to index2009-01-28
Total downloads3 ( #213,563 of 739,303 )
Recent downloads (6 months)0
How can I increase my downloads?