Some theorems on structural entailment relations |
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Authors: | Janusz Czelakowski |
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Affiliation: | 1. Polish Academy of Sciences, Section of Logic, Piotrkowska 179, 90-447, ?ód?
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Abstract: | The classesMatr( ( subseteq ) ) of all matrices (models) for structural finitistic entailments ( subseteq ) are investigated. The purpose of the paper is to prove three theorems: Theorem I.7, being the counterpart of the main theorem from Czelakowski [3], and Theorems II.2 and III.2 being the entailment counterparts of Bloom's results [1]. Theorem I.7 states that if a classK of matrices is adequate for ( subseteq ) , thenMatr( ( subseteq ) ) is the least class of matrices containingK and closed under the formation of ultraproducts, submatrices, strict homomorphisms and strict homomorphic pre-images. Theorem II.2 in Section II gives sufficient and necessary conditions for a structural entailment to be finitistic. Section III contains theorems which characterize finitely based entailments. |
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