Abstract
Let A be a weak Heyting algebra and let \({a, b \in A}\). We give a description for the congruence generated by the pair (a, b), and we use it in order to give a necessary and sufficient condition for a function \({f : A^{k} \rightarrow A}\) to be compatible with every congruence of A. We also find conditions on a not necessarily polynomial function g(a, b) in A that imply that the function \({a \mapsto {\rm min}\{b \in A : g(a, b) \leq b}\}\) is compatible when defined.
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Presented by C. Tsinakis.
This work was partially supported by CONICET Project PIP 112-201101-00636.
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San Martín, H.J. Principal congruences in weak Heyting algebras. Algebra Univers. 75, 405–418 (2016). https://doi.org/10.1007/s00012-016-0381-4
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DOI: https://doi.org/10.1007/s00012-016-0381-4