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===6.43. Reflective Extensions===

===6.43. Reflective Extensions===

This section takes up the topic of reflective extensions in a more systematic fashion, starting from the sign relations <math>L(\text{A})\!</math> and <math>L(\text{B})\!</math> once again and keeping its focus within their vicinity, but exploring the space of nearby extensions in greater detail.

This section takes up the topic of reflective extensions in a more systematic fashion, starting from the sign relations A and B once again and keeping its focus within their vicinity, but exploring the space of nearby extensions in greater detail.

Tables&nbsp;80 and 81 show one way that the sign relations A and B can be extended in a reflective sense through the use of quotational devices, yielding the "first order reflective extensions", Ref1(A) and Ref1(B).

Tables&nbsp;80 and 81 show one way that the sign relations <math>L(\text{A})\!</math> and <math>L(\text{B})\!</math> can be extended in a reflective sense through the use of quotational devices, yielding the ''first order reflective extensions'', <math>\operatorname{Refl}(\text{A})\!</math> and <math>\operatorname{Refl}(\text{B}).\!</math>

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