For propositional logic it can be decided whether a formula has a
deduction from a finite set of other formulas. This volume begins
with a method to decide this for the quantified formulas of those
fragments of arithmetic which express the properties of
order-plus-successor and of order-plus-addition (Pressburger
arithmetic). It makes use of an algorithm eliminating quantifiers
which, in turn, is also applied to obtain consistency proofs for
these fragments.
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