Algebraic real analysis
by
Peter Freyd
University of Pennsylvania

Categorical investigations have disclosed a theory for ``interval algebras''. Its intended model is the closed real interval, identifiable in many categories as-ironically-a final co-algebra. A major theorem is that every algebra of this finitely presented equational theory has a simple quotient and that any simple algebra appears uniquely as a subalgebra of the intended model. This acts as a powerful completeness theorem and allows one to recover-using algebraic techniques-what appears to be a good part of real analysis.

Date received: September 6, 2002