Bulletin of Symbolic Logic 11 (4):526-533 (2005)
|Abstract||We initiate the reverse mathematics of general topology. We show that a certain metrization theorem is equivalent to Π2 1 comprehension. An MF space is defined to be a topological space of the form MF(P) with the topology generated by $\lbrace N_p \mid p \in P \rbrace$ . Here P is a poset, MF(P) is the set of maximal filters on P, and $N_p = \lbrace F \in MF(P) \mid p \in F \rbrace$ . If the poset P is countable, the space MF(P) is said to be countably based. The class of countably based MF spaces can be defined and discussed within the subsystem ACA0 of second order arithmetic. One can prove within ACA0 that every complete separable metric space is homeomorphic to a countably based MF space which is regular. We show that the converse statement, "every countably based MF space which is regular is homeomorphic to a complete separable metric space," is equivalent to Π2 1-CA0. The equivalence is proved in the weaker system Π1 1-CA0. This is the first example of a theorem of core mathematics which is provable in second order arithmetic and implies Π2 1 comprehension|
|Keywords||No keywords specified (fix it)|
|Through your library||Configure|
Similar books and articles
C. Callender & R. Weingard (2000). Topology Change and the Unity of Space. Studies in History and Philosophy of Science Part B 31 (2):227-246.
Josef Berger, Douglas Bridges & Peter Schuster (2006). The Fan Theorem and Unique Existence of Maxima. Journal of Symbolic Logic 71 (2):713 - 720.
Abbas Edalat (1997). Domains for Computation in Mathematics, Physics and Exact Real Arithmetic. Bulletin of Symbolic Logic 3 (4):401-452.
Andrzej W. Jankowski (1985). Disjunctions in Closure Spaces. Studia Logica 44 (1):11 - 24.
H. Jerome Keisler (2006). Nonstandard Arithmetic and Reverse Mathematics. Bulletin of Symbolic Logic 12 (1):100-125.
Laura Crosilla, Hajime Ishihara & Peter Schuster (2005). On Constructing Completions. Journal of Symbolic Logic 70 (3):969 - 978.
Jeffry L. Hirst (1999). Ordinal Inequalities, Transfinite Induction, and Reverse Mathematics. Journal of Symbolic Logic 64 (2):769-774.
Kenneth Schilling & Boško Živaljević (1997). Louveau's Theorem for the Descriptive Set Theory of Internal Sets. Journal of Symbolic Logic 62 (2):595-607.
Stephen G. Simpson (1994). On the Strength of König's Duality Theorem for Countable Bipartite Graphs. Journal of Symbolic Logic 59 (1):113-123.
Mariagnese Giusto & Stephen G. Simpson (2000). Located Sets and Reverse Mathematics. Journal of Symbolic Logic 65 (3):1451-1480.
Sorry, there are not enough data points to plot this chart.
Added to index2009-01-28
Total downloads2 ( #232,382 of 549,064 )
Recent downloads (6 months)0
How can I increase my downloads?