•  25
    Representation of Nonstandard Hulls in IST for Certain Uniform Spaces
    Mathematical Logic Quarterly 37 (13-16): 201-205. 1991.
  •  6
    A remark on uniform spaces with invariant nonstandard hulls
    with Roozbeh Vakil
    Mathematical Logic Quarterly 51 (6): 610-612. 2005.
    Let be a uniform space with its uniformity generated by a set of pseudo-metrics Γ. Let the symbol ≃ denote the usual infinitesimal relation on *X , and define a new infinitesimal relation ≈ on *X by writing x ≈ y whenever *ϱ ≃ *ϱ for each ϱ ∈ Γ and each p ∈ X . We call an S-space if the relations ≃ and ≈ coincide on fin. S -spaces are interesting because their nonstandard hulls have representations within Nelson's internal set theory . This was shown in [1], where it was also observed that the c…Read more
  •  29
    Monadic binary relations and the monad systems at near-standard points
    Journal of Symbolic Logic 52 (3): 689-697. 1987.
    Let ( * X, * T) be the nonstandard extension of a Hausdorff space (X, T). After Wattenberg [6], the monad m(x) of a near-standard point x in * X is defined as m(x) = μ T (st(x)). Consider the relation $R_{\mathrm{ns}} = \{\langle x, y \rangle \mid x, y \in \mathrm{ns} (^\ast X) \text{and} y \in m(x)\}.$ Frank Wattenberg in [6] and [7] investigated the possibilities of extending the domain of R ns to the whole of * X. Wattenberg's extensions of R ns were required to be equivalence relations, amon…Read more