Annual meeting of the Association for Symbolic Logic, New York City, December 1987

S OF PAPERS, NEW YORK CITY, DECEMBER 1987 1289 [2] A. N. KOLMOGOROV, Grundbegriffe der Wahrscheinlichkeitsrechnung, Springer-Verlag, Berlin, 1933, pp. 1-61; English translation, by N. Morrison, Foundations of the theory of probability, Chelsea, New York, 1948. [3] K. R. POPPER, The logic of scientific discovery, H utchinson, London, and Basic Books, New York, 1959. [4] A. RENYI, On a new axiomatic theory of probability, Acta Mathematica Academiae Scientiarum Hungaricae, vol. 6 (1955), pp. 285-335. PAUL BANKSTON, Model-theoretic characterizations of arcs and simple closed curves. Mathematics Department, Marquette University, Milwaukee, Wisconsin 53233. In [3] the authors characterize arcs and simple closed curves, among metrizable spaces, using firstorder properties that hold for the associated lattices of closed sets. That is, if F(X) is the lattice of closed subsets of a metrizable space X, and F(X) satisfies the same first-order sentences as F(arc) (resp. F(simple closed curve)), then X is an arc (resp. a simple closed curve). Our result [1] resembles the above in form; it characterizes arcs and simple closed curves, among locally connected compact metrizable spaces, using positive-bounded properties (a la [2]) that approximately hold for the associated Banach spaces of continuous real-valued functions.