Number Systems with Simplicity Hierarchies: A ... - Ohio University
Number Systems with Simplicity Hierarchies: A ... - Ohio University
Number Systems with Simplicity Hierarchies: A ... - Ohio University
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1238 PHILIP EHRLICH<br />
XL, XR, YL, and yRrange over the members of Ls(x), Rs(x), Ls(Y), and Rs(Y), respectively.<br />
DEFINITION OF X + Y.<br />
DEFINITION OF-X.4<br />
DEFINITION OF Xy.<br />
x + y {X +LYy,X+ YL XR+ yX+yR}.<br />
-X = {xR I -X L}<br />
xy {xLy + xyLXLyLxRy + xyR R R y<br />
x y + xy -x YRXY + xyL _xRyL}.<br />
1.4. s-Hierarchical embeddings and complete s-hierarchical ordered algebraic structures.<br />
The present subsection culminates in a theorem that indicates that (No,
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