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A theory of hyperfinite sets
Annals of Pure and Applied Logic 143 (1-3):3-19 (2006)
Abstract
We develop an axiomatic set theory — the Theory of Hyperfinite Sets THS— which is based on the idea of the existence of proper subclasses of large finite sets. We demonstrate how theorems of classical continuous mathematics can be transfered to THS, prove consistency of THS, and present some applicationsLinks
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Citations of this work
The notion of process in nonstandard theory and in Whiteheadian metaphysics.Stathis Livadas - 2013 - Manuscrito 36 (1):103-137.
On Finite Approximations of Topological Algebraic Systems.L. Yu Glebsky, E. I. Gordon & C. Ward Hensen - 2007 - Journal of Symbolic Logic 72 (1):1 - 25.
References found in this work
Existence and feasibility in arithmetic.Rohit Parikh - 1971 - Journal of Symbolic Logic 36 (3):494-508.
On the strength of nonstandard analysis.C. Ward Henson & H. Jerome Keisler - 1986 - Journal of Symbolic Logic 51 (2):377-386.
The strength of nonstandard methods in arithmetic.C. Ward Henson, Matt Kaufmann & H. Jerome Keisler - 1984 - Journal of Symbolic Logic 49 (4):1039-1058.
Internal Set Theory: A New Approach to Nonstandard Analysis.Edward Nelson - 1977 - Journal of Symbolic Logic 48 (4):1203-1204.
Internal approach to external sets and universes.Vladimir Kanovei & Michael Reeken - 1995 - Studia Logica 55 (2):347 - 376.
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