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pp-elimination of quantifiers in module theories
Novák, Jindřich ; Šaroch, Jan (advisor) ; Ježil, Ondřej (referee)
The aim of this thesis is to prove the Baur-Monk Theorem and thereby show complete module-theories admit an elimination of quantifiers down to (Boolean combinations of) existential formulae. To achieve this, following a brief introduction in Chapter 1, the reader is fami- liarised in Chapter 2 with the notion of a positive-primitive formula in the lan- guage of right R-modules, and its close relationship with commutative groups, their cosets, and lattices. Chapter 3 first lays the technical groundwork for the proof of the Baur-Monk Theorem, presented in Section 3.3, in its opening two subsections which contain the needed combinatorial and group-theoretical results, namely the Neumann Lemma and a variation on the Inclusion-Exclusion Principle. Chapter 4 concludes the mathematical work contained herein with a brief over- view of some immediate corollaries of the the Baur-Monk Theorem and earlier results.
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