Creating and sharing knowledge for telecommunications

Quantifier elimination revisited

by IT on 11-01-2013
João Rasga, IST-UTL / SQIG-IT

January 11, 2013, Friday, 16h15m.
Room: 4.35, Mathematics (please note the exceptional room).

Abstract: Sufficient conditions for a first-order theory to be 1-model-complete and for having algebraically prime models are proposed. These conditions can be used to prove that a given theory Θ enjoys quantifier elimination, taking into account the following well known criteria for quantifier elimination: If Θ is 1-model-complete; and Θ has algebraically prime models; then Θ enjoys quantifier elimination. The applicability of these new conditions is illustrated on the theory of the natural numbers with successor and on the theory of algebraically closed fields. The talk reports on ongoing joint work with Cristina Sernadas.

Support: SQIG/Instituto de Telecomunicações with support from FCT and FEDER namely by the FCT project PEst-OE/EEI/LA0008/2011.