In this paper we propose a new lifetime model, called the odd generalized exponential gompertz distribution. We obtained some of its mathematical properties. Some structural properties of the new distribution are studied. The method of maximum likelihood is used for estimating the model parameters and the observed Fisher's information matrix is derived. We illustrate the usefulness of the proposed model by applications to real data.

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Computably enumerable equivalence relations (ceers) received a lot of attention in the literature. The standard tool to classify ceers is provided by the computable reducibility ďc. This gives rise to a rich degree-structure. In this paper, we lift the study of c-degrees to the ∆ 0 2 case. In doing so, we rely on the Ershov hierarchy. For any notation a for a non-zero computable ordinal, we prove several algebraic properties of the degree-structure induced by ďc on the Σ´1 a Π´1 a equivalence relations. A special focus of our work is on the (non)existence of infima and suprema of c-degrees.

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