On partial disjunction properties of theories containing Peano arithmetic

摘要

Let G be a class of formulas. We say that a theory T in classical logic has the G -disjunction property if for any G sentences. and., either T or T whenever T phi v psi. First, we characterize the G -disjunction property in terms of the notion of partial conservativity. Secondly, we prove a model theoretic characterization result for Sn-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.