Definability and Universal Algebra

CAMPERCHOLI, MIGUEL

Buenos Aires

Congreso; 16th Latin American Symposium on Mathematical Logic; 2014

In our talk we will introduce several (semantical) characterizations of definability, each concerning a specific format of first order formulas, e.g., definability by conjunctions of atomic formulas. We will show aswell how these characterizations can be applied to address interesting questions in the realm of universal algebra. For instance, to the definability of principal congruences and term interpolation results akin to the theorems of Baker and Pixley [1, 2]. References [1] Baker, K. and Pixley, A., Polynomial interpolation and the Chinese Re- mainder Theorem for algebraic systems, Mathematische Zeitschrift 143, pp. 165?174, 1975. [2] Pixley, A., The ternary discriminator function in universal algebra, Mathematische Annalen 191, pp. 167?180, 1971.