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We isolate a \u2018uniform\u2019 fragment of our equational logic, which corresponds to the nominal logics present in the literature. We give semantically invariant translations of theories for nominal algebra and NEL into \u2018uniform\u2019 theories, and systematically prove HSP theorems for models of these theories.<\/jats:p>","DOI":"10.1017\/s0960129509990399","type":"journal-article","created":{"date-parts":[[2010,3,25]],"date-time":"2010-03-25T06:27:46Z","timestamp":1269498466000},"page":"285-318","source":"Crossref","is-referenced-by-count":11,"title":["On universal algebra over nominal sets"],"prefix":"10.1017","volume":"20","author":[{"given":"ALEXANDER","family":"KURZ","sequence":"first","affiliation":[]},{"given":"DANIELA","family":"PETRI\u015eAN","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2010,3,25]]},"reference":[{"key":"S0960129509990399_ref17","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2007.09.024"},{"key":"S0960129509990399_ref16","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0927-0","volume-title":"Sheaves in Geometry and Logic: A First Introduction to Topos Theory (Universitext)","author":"Mac Lane","year":"1994"},{"key":"S0960129509990399_ref15","unstructured":"Kurz A. and Rosick\u00fd J. 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