Classical Modal De Morgan Algebras

In this note we introduce the variety ${{\mathcal C}{\mathcal D}{\mathcal M}_\square}$ of classical modal De Morgan algebras as a generalization of the variety ${{{\mathcal T}{\mathcal M}{\mathcal A}}}$ of Tetravalent Modal algebras studied in [11]. We show that the variety ${{\mathcal V}_0}$ defined by H. P. Sankappanavar in [13], and the variety S of Involutive Stone algebras introduced by R. Cignoli and M. S de Gallego in [5], are examples of classical modal De Morgan algebras. We give a representation theory, and we study the regular filters, i.e., lattice filters closed under an implication operation. Finally we prove that the variety ${{{\mathcal T}{\mathcal M}{\mathcal A}}}$ has the Amalgamation Property and the Superamalgamation Property.     

Frontal Operators in Weak Heyting Algebras

In this paper we shall introduce the variety FWHA of frontal weak Heyting algebras as a generalization of the frontal Heyting algebras introduced by Leo Esakia in [10]. A frontal operator in a weak Heyting algebra A is an expansive operator τ preserving finite meets which also satisfies the equation ${\tau(a) \leq b \vee (b \rightarrow a)}$ , for all ${a, b \in A}$ . These operators were studied from an algebraic, logical and topological point of view by Leo Esakia in [10]. We will study frontal operators in weak Heyting algebras and we will consider two examples of them. We will give a Priestley duality for the category of frontal weak Heyting algebras in terms of relational spaces ${\langle X, \leq, T, R \rangle}$ where ${\langle X, \leq, T \rangle}$ is a WH-space [6], and R is an additional binary relation used to interpret the modal operator. We will also study the WH-algebras with successor and the WH-algebras with gamma. For these varieties we will give two topological dualities. The first one is based on the representation given for the frontal weak Heyting algebras. The second one is based on certain particular classes of WH-spaces.     

A Structural Analysis of the Obsessional Character: A Fairbairnian Perspective

This paper reviews the object relations model of W.R.D. Fairbairn and applies it to the understanding of the obsessional personality. Fairbairn's model sees attachment to good objects as the immutable component of normal development. Parental failures are seen as intolerable to the child and trigger the splitting defense that isolates (via repression) the frustrating aspects of the object along with the part of the child's ego that relates only to that part-object. This fundamental defense protects the child from the knowledge that he is dependent on indifferent objects and preserves his attachment. The split-off part-self and part-object structures are too disruptive to remain conscious, yet despite being repressed make themselves known through repetition compulsions and transference. The specific characteristics of families that produce obsessional children impact the child's developing ego structures in similar ways. This style of developmental history creates predictable self and object configurations in the inner world, which then translate via repetition compulsion into obsessional behavior in adulthood.