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Topic: Ultraproduct

	Ultraproduct -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-22)
		Certainly the most important case is the construction of the (Click link for more info and facts about hyperreal numbers) hyperreal numbers by taking the ultraproduct of countably infinitely many copies of the field of (Any rational or irrational number) real numbers.
		The (Click link for more info and facts about hyperreal numbers) hyperreal numbers are the ultraproduct of one copy of the (Any rational or irrational number) real numbers for every natural number, with regard to an ultrafilter containing all cofinite sets of natural numbers.
		Analogously, you could define (Click link for more info and facts about nonstandard complex numbers) nonstandard complex numbers by taking the ultraproduct of copies of the field of (A number of the form a+bi where a and b are real numbers and i is the square root of -1) complex numbers.
	www.absoluteastronomy.com /encyclopedia/u/ul/ultraproduct.htm (479 words)

	First-order Model Theory
		If we have an ultrafilter U over I, then we can construct a reduced product from C by making two elements of C equivalent if and only if the set of indices at which they are equal is a set in the ultrafilter U.
		This is indeed an equivalence relation on the domain of C, and the resulting reduced product is called an ultraproduct of the factors of C.
		If C is a power of A then this ultraproduct is called an ultrapower of A, and it is sometimes written U-prod A.
	plato.stanford.edu /entries/modeltheory-fo (6179 words)

	ipedia.com: Field (mathematics) Article (Site not responding. Last check: 2007-10-22)
		If I is an index set, U is an ultrafilter on I, and F
		is a field for every i in I, the ultraproduct of the F
		The hyperreal numbers form a field containing the reals, plus infinitesimal and infinite numbers.
	www.ipedia.com /field__mathematics_.html (1287 words)

	MSCS Faculty (alphabetic order) (Site not responding. Last check: 2007-10-22)
		Modeling non-intersective adjectives using operator logis, The review of Modern Logic, vol.
		A survey of ultraproduct constructions in general topology, Topology Atlas Invited Contributions, vol.
		Linear Hypothesis in Errors in Variables Model; Slope Parameters in Errors-in-Variables Models; Bayesian Statistics; Normal Distribution; Invariance Minimaxity.
	www.mscs.mu.edu /faculty_research_alpha.html (1321 words)

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