@article {IOPORT.05161537,
    author       = {Mummert, Carl},
    title        = {Reverse mathematics of MF spaces.},
    year         = {2006},
    journal      = {Journal of Mathematical Logic},
    volume       = {6},
    number       = {2},
    issn         = {0219-0613},
    pages        = {203-232},
    publisher    = {World Scientific Publishing Company, Singapore; Singapore University Press, National University of Singapore, Singapore},
    doi          = {10.1142/S0219061306000578},
    abstract     = {This paper provides the foundation for the reverse mathematics of countably based MF (maximal filter) spaces. Previously, reverse mathematics considered results on complete separable metric spaces, but this formulation extends the program to broader classes of spaces and results. In particular, metrization theorems can be formalized in this setting. A number of equivalence results involving atypically strong comprehension axioms are proved here. For example, the proposition that every regular countably based MF space is homeomorphic to a complete separable metric space is shown to be equivalent to $\Pi^1_2$-CA$_0$ over $\Pi^1_1$-CA$_0$. Also, the statement ``every uncountable closed subset of a countably based MF space contains a perfect set'' is proved to be equivalent to ``for every subset $A$ of the natural numbers, $\aleph^{L(A)}_1$ is countable.'' The material presented here includes work from the author's Ph.D.~thesis and provides details of arguments sketched in {\it C. Mummert} and {\it S. G. Simpson}'s paper ``Reverse mathematics and $\Pi^1_2$ comprehension" [Bull. Symb. Log. 11, No. 4, 526--533 (2005; Zbl 1106.03050)].},
    reviewer     = {Jeffry L. Hirst (Boone)},
    identifier   = {05161537},
}