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+ <TITLE>HOL/Hyperreal/README</TITLE>
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-<H2>Hyperreal--Ultrafilter Construction of the Non-Standard Reals</H2>
+<H2>Hyperreal: Ultrafilter Construction of the Non-Standard Reals</H2>
See J. D. Fleuriot and L. C. Paulson. Mechanizing Nonstandard Real
Analysis. LMS J. Computation and Mathematics 3 (2000), 140-190.
-<UL>
-<LI><A HREF="Zorn.html">Zorn</A>
-Zorn's Lemma: proof based on the ZF version.
-<LI><A HREF="Filter.html">Filter</A>
+ <UL>
+ <LI><A HREF="Filter.html">Filter</A>
Theory of Filters and Ultrafilters.
Main result is a version of the Ultrafilter Theorem proved using
Zorn's Lemma.
-<LI><A HREF="HyperDef.html">HyperDef</A>
+
+ <li><A HREF="HLog.html">HLog</A> Non-standard logarithms
+ <li><a href="HSeries.html">HSeries</a> Non-standard theory of finite summation and infinite series
+ <li><a href="HTranscendental.html">HTranscendental</a> Non-standard extensions of transcendental functions
+ <LI><A HREF="HyperDef.html">HyperDef</A>
Ultrapower construction of the hyperreals
-<LI><A HREF="NSA.html">NSA</A>
-Theory defining sets of infinite numbers, infinitesimals,
-the infinitely close relation, and their various algebraic properties.
-
-<LI><A HREF="HyperNat.html">HyperNat</A>
-Ultrapower construction of the hypernaturals
-
-<LI><A HREF="HyperPow.html">HyperPow</A>
-Powers theory for the hyperreals
-
-<LI><A HREF="Star.html">Star</A>
-Nonstandard extensions of real sets and real functions
-<LI><A HREF="NatStar.html">NatStar</A>
-Nonstandard extensions of sets of naturals and functions on the natural
-numbers
-
-<LI><A HREF="SEQ.html">SEQ</A>
-Theory of sequences developed using standard and nonstandard analysis
+ <li><a href="HyperNat.html">HyperNat</a> Ultrapower construction of the hypernaturals
+ <li><a href="HyperPow.html">HyperPow</a> Powers theory for the hyperreals
+ <li><a href="IntFloor.html">IntFloor</a> Floor and Ceiling functions relating the reals and integers
+ <li><a href="Integration.html">Integration</a> Gage integrals
+ <li><a href="Lim.html">Lim</a> Theory of limits, continuous functions, and derivatives
+
+ <LI><a href="Log.html">Log</a> Logarithms for the reals
+
+ <li><a href="MacLaurin.html">MacLaurin</a> MacLaurin series
+
+ <li><a href="NatStar.html">NatStar</a> Star-transforms for the hypernaturals, to form non-standard extensions of sets and functions involving the naturals or reals
+ <li><a href="NthRoot.html">NthRoot</a> Existence of n-th roots of real numbers
+ <li><a href="NSA.html">NSA</a> Theory defining sets of infinite numbers, infinitesimals, the infinitely close relation, and their various algebraic properties.
+ <li><a href="Poly.html">Poly</a> Univariate real polynomials
+ <li><a href="SEQ.html">SEQ</a> Convergence of sequences and series using standard and nonstandard analysis
+ <li><a href="Series.html">Series</a> Finite summation and infinite series for the reals
+ <li><a href="Star.html">Star</a> Nonstandard extensions of real sets and real functions
+ <li><a href="Transcendental.html">Transcendental</a> Power series and transcendental functions
+ </UL>
+ <P>Last modified on $Date$
-<LI><A HREF="Lim.html">Lim</A>
-Theory of limits, continuous functions, and derivatives
-<LI><A HREF="Series.html">Series</A>
-Standard theory of finite summation and infinite series
-
-</UL>
-
-<P>Last modified on $Date$
-
-<HR>
+ <HR>
<ADDRESS>
<A NAME="lcp@cl.cam.ac.uk" HREF="mailto:lcp@cl.cam.ac.uk">lcp@cl.cam.ac.uk</A>