Hyperreal--Ultrafilter Construction of the Non-Standard Reals
See J. D. Fleuriot and L. C. Paulson. Mechanizing Nonstandard Real
Analysis. LMS J. Computation and Mathematics 3 (2000), 140-190.
- Zorn
Zorn's Lemma: proof based on the ZF version.
- Filter
Theory of Filters and Ultrafilters.
Main result is a version of the Ultrafilter Theorem proved using
Zorn's Lemma.
- HyperDef
Ultrapower construction of the hyperreals
- NSA
Theory defining sets of infinite numbers, infinitesimals,
the infinitely close relation, and their various algebraic properties.
- HyperNat
Ultrapower construction of the hypernaturals
- HyperPow
Powers theory for the hyperreals
- Star
Nonstandard extensions of real sets and real functions
- NatStar
Nonstandard extensions of sets of naturals and functions on the natural
numbers
- SEQ
Theory of sequences developed using standard and nonstandard analysis
- Lim
Theory of limits, continuous functions, and derivatives
- Series
Standard theory of finite summation and infinite series
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