When is an alter ego a minimal dualizing structure?

We show that a particular five-element algebra is dualized by a particular alter-ego. We also show that, in some limited sense, the alter ego we chose is minimal. The algebra that we examine is a f0;1g-valued unary algebra with 0. It has meet and join as homomorphisms.algebrafive-elementdualizedalter egofinite unar

Rank and duality of escalator algebras.

We define a specific family of finite bi-unary algebras called escalator algebras. These algebras were introduced in the work of Hyndman and Willard [9] and Little [10]. We show that they have infinite rank, are dualizable but are not strongly dualizable.The original print copy of this thesis may be available here: http://wizard.unbc.ca/record=b123050

On the dualisabilty of finite {0, 1 }-valued unary algebras with zero.

This thesis provides a few results regarding the natural dualisability of certain {0, 1}-valued unary algebras with zero. We use pp-formulae to develop a sufficient criterion for non-dualisability of such algebras. With this criterion, we show that {0, 1}-valued unary algebras with zero with unique rows whose rows form an order ideal (with respect to the lattice order {0, 1}ⁿ under 0 < 1) are not dualisable if its rows do not form an lattice order. For the case where the rows do form a lattice, we use the Interpolation Condition to show that the algebra is dualisable. The last result of this thesis provides another sufficient criterion for non-dualisability by looking at two-term reducts. --Leaf ii.The original print copy of this thesis may be available here: http://wizard.unbc.ca/record=b195332

HOW FINITE IS A THREE-ELEMENT UNARY ALGEBRA?

We show that, within the class of three-element unary algebras, there is a tight connection between a finitely based quasi-equational theory, finite rank, enough algebraic operations (from natural duality theory) and a special injectivity condition