The Union of Chemistry and Physics by Hinne Hettema

Author:Hinne Hettema
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

2. ;

3.There exist 〈x i , x〉, 〈y i , y〉 ∈ L such that: (i) and ; and

(ii) and .

6.5.4 Reducing Links

We now turn to the concept of a reducing link. There are of course some differences between the structuralist conception of reduction and reducing links. Simply put, the difference is that a full structuralist reduction specifies a global relationship between entire structures (and hence is based on what we have called an abstract link above), whereas a link potentially specifies only a partial relationship between structures (and is potentially based on the notion of a concrete link). Designate the relevant subset of models by . is a restriction on the full reducing theory.

Hence, we need a notion of reduction based on the idea of a concrete link. This can be achieved by suitably adapting the concept of the restricted theory .

In cases where the reducing link is based on an abstract link, the structure can be defined as a subset of . In the cases where it is based on a concrete link, the members of are ‘stripped’ of those terms that do not participate in the concrete link.

The requirements for a reducing abstract link are:

Definition 22 (Reducing abstract link)

L is an reducing link from to iff: 1.There exists some subset of such that: (i) ;

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