Foundations of the Theory of Parthood by Andrzej Pietruszczak

Author:Andrzej Pietruszczak
Language: eng
Format: epub
ISBN: 9783030365332
Publisher: Springer International Publishing

Therefore, in accordance with our analysis in Sect. 3.2, we can define the partial operation . We can also use the fact that , from which we get:

We bear in mind that the reciprocal definability of relations and , () holds. Therefore, condition () also is satisfied.

Having condition () we can once again “extend” Theorems 3.9.6 and 3.9.8:

Theorem 3.9.10

The following identities of classes of structures hold:

Proof

By virtue of Corollary 2.​6.​9, in the class condition (resp. ()) entails condition (). By virtue of Theorem 3.2.3, conditions (), () and () also entail (). We therefore apply Theorem 3.9.6.

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