Robert S. Lubarsky

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BD-N is a weak principle of constructive analysis. Several interesting principles implied by BD-N have already been identified, namely the closure of the anti-Specker spaces under product, the Riemann Permutation Theorem, and the Cauchyness of all partially Cauchy sequences. Here these are shown to be strictly weaker than BD-N, yet not provable in set(More)
In order to build the collection of Cauchy reals as a set in constructive set theory, the only power set-like principle needed is exponentiation. In contrast, the proof that theDedekind reals form a set has seemed to requiremore than that. Themain purpose here is to show that exponentiation alone does not suffice for the latter, by furnishing a Kripke model(More)
When making the transition from a classical to an intuitionistic system, one is compelled to reconsider the axioms chosen. For instance, it would be natural to re-formulate those that imply Excluded Middle. In the context of set theory, typically the Axiom of Foundation is substituted by the Axiom of Set Induction, the two being equivalent classically but(More)
Some models of set theory are given which contain sets that have some of the important characteristics of being geometric, or spatial, yet do not have any points, in various ways. What’s geometrical is that there are functions to these spaces defined on the ambient spaces which act much like distance functions, and they carry normable Riesz spaces which act(More)
We give the natural topological model for ¬BD-N, and use it to show that the closure of spaces with the anti-Specker property under product does not imply BD-N. Also, the natural topological model for ¬BD is presented. Finally, for some of the realizability models known indirectly to falsify BD-N, it is brought out in detail how BD-N fails. keywords:(More)