Abstract
We present a scheme for providing axiomatizations of universal classes. We use infinitary sentences there. New proofs of Birkhoff’s \(\mathsf {HSP}\)-theorem and Mal’cev’s \(\mathsf {SPP_U}\)-theorem are derived. In total, we present 75 facts of this sort.
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To the memory of Bjarni Jónsson.
This article is part of the topical collection “In memory of Bjarni Jónsson” edited by J.B. Nation.
The work was supported by the Polish National Science Centre Grant no. DEC-2011/01/D/ST1/06136.
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Stronkowski, M.M. Axiomatizations of universal classes through infinitary logic. Algebra Univers. 79, 26 (2018). https://doi.org/10.1007/s00012-018-0507-y
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DOI: https://doi.org/10.1007/s00012-018-0507-y