Infinitary logic and topological homeomorphisms

For a suitable infinitary language for topology, a family of sentences will be considered which is large enough to determine countable, second-countable topological spaces up to homeomorphism. Yet at the same time, th.s family is small enough that its sentences can not distinguish between the usual topologies on the reals and rationals. (A subsequent article will show that, for finitary sentences, the sentences of this family are those whose truth is preserved between equivalent topological bases.) The author wishes to acknowledge helpful conversations with Professors K. J. BARWISE, IF. J. KEISLER, and K. KUNEN. In particular, Prof. KENEN suggested the topological precursor of Theorem 4.