Directly Indecomposables in Semidegenerate Varieties of Connected po-Groupoids
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We study varieties with a term-definable poset structure, po-groupoids. It is known that connected posets have the strict refinement property (SRP). In Sánchez Terraf and Vaggione (Trans Am Math Soc, in press) 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.
KeywordsConnected poset Strict refinement property Semidegenerate variety Definable factor congruences
Mathematics Subject Classifications (2000)06A12 20M10
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