Directly Indecomposables in Semidegenerate Varieties of Connected po-Groupoids

Details Directly Indecomposables in Semidegenerate Varieties of Connected po-Groupoids Directly Indecomposables in Semidegenerate Varieties of Connected po-Groupoids

2008-10-07

arxiv.org/abs/0810.1305v1

Order, 25 Issue 4 (2008) p. 377

Mathematics

Logic

Scientific paper

10.1007/s11083-008-9101-9

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.

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