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10$\Sigma^1_1$ -Completeness of a Fragment of the Theory of Trees with Subtree RelationNotre Dame Journal of Formal Logic 35 (3): 426-432. 1994.We consider the structure of all labeled trees, called also infinite terms, in the first order language with function symbols in a recursive signature of cardinality at least two and at least a symbol of arity two, with equality and a binary relation symbol which is interpreted to be the subtree relation. The existential theory over of this structure is decidable (see Tulipani [9]), but more complex fragments of the theory are undecidable. We prove that the theory of the structure is in , where …Read more
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8Σ11-completeness Of A Fragment Of The Theory Of Trees With Subtree RelationNotre Dame Journal of Formal Logic 35 (3): 426-432. 1994.We consider the structure $IT_S$ of all labeled trees, called also infinite terms, in the first order language ${\cal L}$ with function symbols in a recursive signature $S$ of cardinality at least two and at least a symbol of arity two, with equality and a binary relation symbol $\sqsubseteq$ which is interpreted to be the subtree relation. The existential theory over ${\cal L}$ of this structure is decidable, but more complex fragments of the theory are undecidable. We prove that the $ \exists\…Read more
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6Low sets without subsets of higher many-one degreeMathematical Logic Quarterly 57 (5): 517-523. 2011.Given a reducibility ⩽r, we say that an infinite set A is r-introimmune if A is not r-reducible to any of its subsets B with |A\B| = ∞. We consider the many-one reducibility ⩽m and we prove the existence of a low1 m-introimmune set in Π01 and the existence of a low1 bi-m-introimmune set
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11Sets without Subsets of Higher Many-One DegreeNotre Dame Journal of Formal Logic 46 (2): 207-216. 2005.Previously, both Soare and Simpson considered sets without subsets of higher -degree. Cintioli and Silvestri, for a reducibility , define the concept of a -introimmune set. For the most common reducibilities , a set does not contain subsets of higher -degree if and only if it is -introimmune. In this paper we consider -introimmune and -introimmune sets and examine how structurally easy such sets can be. In other words we ask, What is the smallest class of the Kleene's Hierarchy containing -intro…Read more
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Università degli Studi di CamerinoResearcher
Camerino, Italy