An Attempt of the Ego's Axiomatic Conception

Psychologists use identity's and Ego's conceptions. The first conception is not clear, the second one from logical point of view is not correct. The aim of this article is to provide the definition of these two conceptions. Let: 1. P(=) is psychological (logical) identity's indication 2. o, o(1), o(2),..) (e, e(1), e(2),..) are people's (Ego's) variables 3. j is the function's indication. The expressions: j(o) (j (o(i))), dla i>0, we read: person's Ego o (o(i)). The psychological identity's definition provided in the article is as follows: (P-1) for all o (oPo), (P2) for all o(1)for all o(2) (o(1)Po(2) -> o(2)Po(1)), (P3) for all o(1)for all o(2) for all o(3) (o(1)Po(2) boolean AND o(2)Po(3) -> o(1)Po(3)) (P4) for all o for all o(1)for all o(2)for all o(3)for all R [(oRo) boolean AND (o(1)Ro(2) -> o(2)Ro(1)) boolean AND (o(1)Ro(2) boolean AND o(2)Ro(3) -> o(1)Ro(3)) boolean AND (o(1)Po(2) -> o(1)Ro(2))]. And the Ego is defined as follows: (I) for all e (e = e), (J(1)) for all e there exists o [j(o) = e], (J(2)) for all a there exists o [j(o) = e], (J(3)) for all o(1)for all o(2) [j(o(1)) = j(o(2)) o(1)Po(2)], (J(4)) for all e for all o (e # o), (J(5)) for all e for all o similar to (ePo), (J(6)) for all e(1)for all e2 similar to (e(1)Pe(2)).