Infinitary simultaneous recursion theorem

We prove an in nitary version of the Double Recursion Theorem of Smullyan. We give some applications which show how this form of the Recursion Theo- rem can be naturally applied to obtain interesting in nite sequences of pro- gramsPeer Reviewe

Directly Indecomposables in Semidegenerate Varieties of Connected po-Groupoids

We study varieties with a term-definable poset structure, "po-groupoids". It is known that connected posets have the "strict refinement property" (SRP). In [arXiv:0808.1860v1 [math.LO]] it is proved that semidegenerate varieties with the SRP have definable factor congruences and if the similarity type is finite, directly indecomposables are axiomatizable by a set of first-order sentences. We obtain such a set for semidegenerate varieties of connected po-groupoids and show its quantifier complexity is bounded in general

Boolean like algebras

Using Vaggione’s concept of central element in a double pointed algebra, we introduce the notion of Boolean like variety as a generalization of Boolean algebras to an arbitrary similarity type. Appropriately relaxing the requirement that every element be central in any member of the variety, we obtain the more general class of semi-Boolean like varieties, which still retain many of the pleasing properties of Boolean algebras. We prove that a double pointed variety is discriminator i↵ it is semi-Boolean like, idempotent, and 0-regular. This theorem yields a new Maltsev-style characterization of double pointed discriminator varieties. Moreover, we show that every idempotent semi-Boolean-like variety is term equivalent to a variety of noncommutative Boolean algebras with additional regular operations

Infinitary simultaneous recursion theorem

We prove an in nitary version of the Double Recursion Theorem of Smullyan. We give some applications which show how this form of the Recursion Theo- rem can be naturally applied to obtain interesting in nite sequences of pro- gramsPeer Reviewe

A note on congruence systems of MS-algebras

summary:Let $L$ be an MS-algebra with congruence permutable skeleton. We prove that solving a system of congruences $(\theta _{1},\ldots ,\theta _{n};x_{1} ,\ldots ,x_{n})$ in $L$ can be reduced to solving the restriction of the system to the skeleton of $L$, plus solving the restrictions of the system to the intervals $[x_{1},\bar{\bar{x}}_{1}],\dots ,[x_{n},\bar{ \bar{x}}_{n}].