### Congruence extension property for ordered algebras (Valdis Laan, NBSAN York, 20th November 2013)

**Abstract:**
An ordered universal algebra is an universal algebra equipped
with an order relation such that all operations are monotone. In the case
of ordered algebras there are two important types of equivalence relations:
so called order-congruences and lax congruences.
We say that an ordered algebra A has congruence extension property
(CEP) if any order-congruence on any subalgebra B of A is a restriction of
an order-congruence on A. Similarly one can define the lax congruence
extension property (LEP). In our talk we discuss some basic results about
these two properties.