On partial disjunction properties of theories containing Peano arithmetic

Archive for Mathematical Logic 57 (7-8):953-980 (2018)
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Abstract

Let \ be a class of formulas. We say that a theory T in classical logic has the \-disjunction property if for any \ sentences \ and \, either \ or \ whenever \. First, we characterize the \-disjunction property in terms of the notion of partial conservativity. Secondly, we prove a model theoretic characterization result for \-disjunction property. Thirdly, we investigate relationships between partial disjunction properties and several other properties of theories containing Peano arithmetic. Finally, we investigate unprovability of formalized partial disjunction properties.

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References found in this work

The incompleteness theorems.Craig Smorynski - 1977 - In Jon Barwise (ed.), Handbook of mathematical logic. New York: North-Holland. pp. 821 -- 865.
On the interpretation of intuitionistic number theory.S. C. Kleene - 1945 - Journal of Symbolic Logic 10 (4):109-124.
Zum intuitionistischen aussagenkalkül.K. Gödel - 1932 - Anzeiger der Akademie der Wissenschaften in Wien 69:65--66.

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