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EN
CONTENTS Introduction........................................................................................................................................................................................................................5 0. Terminology and preliminaries......................................................................................................................................................................................12 1. The extent of cut elimination by absorption..................................................................................................................................................................17 2. ∏¹-completeness of second order logic and a new proof of the normal form theorem.................................................................................................24 3. Weak models and proper three-valued models of second order theories....................................................................................................................31 4. Model theoretic proofs of the normal form theorem for higher order systems: comparison with the literature..............................................................39 5. Completeness of the systems $JT^n$ and $∏^n$-completeness of $∑^n$-theories.....................................................................................................43 6. ∀-analytical completeness of the systems $JPRE^n$ and poor completeness of the theories $PRE^n$ of primitive recursive equations....................48 7. ∀¹ ∃⁰-completeness of PRE² and König's Lemma for primitive recursive 0-1-trees......................................................................................................56 References.......................................................................................................................................................................................................................62
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