Portugaliæ Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 52, No. 3, pp. 331-336 (1995)

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A Note on a Result of Buss Concerning Bounded Theories and the Collection Scheme

Fernando Ferreira

Universidade de Lisboa, Departamento de Matemática,
Rua Ernesto de Vasconcelos, Bloco C1, 3, 1700 Lisboa - PORTUGAL
E-mail: ferferr@ptmat.lmc.fc.ul.pt

Abstract: Samuel Buss showed that, under certain circumstances, adding the collection scheme for bounded formulae to a bounded theory of arithmetic yields a $\forall\Sigma_{1}$-conservative extensions. We present a very simple model theoretic proof of a generalization of this result.

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