# A Cantor-Bernstein type theorem for effect algebras - download pdf or read online

By Jenca G.

We end up that if E1 and E2 are a-complete influence algebras such that E1 is an element of E2 and E2 is an element of E1, then E1 and E2 are isomorphic.

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1. action;:> Fig.!.!. Schema of an individual with pragmatic cognition in a situation with goal and means. We express symbolically the relation between a goal and a means by an arrow with a switch. First, an individual calculates the utility of reaching his goal without using a certain means (the switch is off); then he 36 V. A. Lefebvre, Algebra of Conscience © Springer Science+Business Media Dordrecht 2001 MORAL COGNITION 37 calculates the utility using the means (the switch is on). He compares the results and makes the 'optimal' decision.

Individuals of the non-sacrificial type (opportunist and hypocrite) in the first ethical system manifest aggressive behavior, while in the second ethical system they tend toward compromise. All the above types are established based on three-tier formulae of individuals. Further, we demonstrate that for analysis of formulae of arbitrary complexity the value of the ethical statuses may be taken as a basis. We introduce the concept of the 'perfect individual' whose ethical status is equal to 1. Such an individual cannot 'see' himself as perfect.

The axioms above can be made to correspond in a natural way to the following Boolean expressions: ETHICAL SYSTEMS AND BOOLEAN ALGEBRA I (1)1+0=1 45 II (2) 1 • 0 = 0 1. 0 = 0 1+0=1 (3) 1 + 1 = 1 1• 1= 1 (4)0+0=0 0. 0 = 0 (5)0~0= 1 We see that in the first ethical system '+' is taken as the sign of confrontation, and '•' is the sign of compromise. In the second ethical system the opposite is true: '+' is the sign of compromise, and '•' the sign of confrontation. Axioms (1) and (2) reflect the specific of interaction between good and evil.

### A Cantor-Bernstein type theorem for effect algebras by Jenca G.

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