We show that Intuitionistic Open Induction iop is not closed under the rule DNS(∃1 ). This is established by constructing a Kripke model of iop+¬Ly(2y > x), where Ly(2y > x) is universally quantified on x. On the other hand, we prove that iop is equivalent with the intuitionistic theory axiomatized by PA− plus the scheme of weak ¬¬LNP for open formulas, where universal quantification on the par...

In this paper we study the properties of systems of bounded arithmetic capturing small complexity classes and state conditions sufficient for such systems to capture the corresponding complexity class tightly. Our class of systems of bounded arithmetic is the class of secondorder systems with comprehension axiom for a syntactically restricted class of formulas Φ ⊂ Σ 1 based on a logic in the de...

There has been much prior work on understanding the complexity of the constraint satisfaction problem (CSP), a broad framework capturing many combinatorial problems. This paper studies the complexity of the quantified constraint satisfaction problem (QCSP), a natural and strict generalization of the CSP. The CSP can be viewed as the problem of deciding whether or not existentially quantified fo...

Binary transitive closure logic (FO∗ for short) is the extension of first-order predicate logic by a transitive closure operator of binary relations. Deterministic binary transitive closure logic (FOD∗) is the restriction of FO∗ to deterministic transitive closures. It is known that these logics are more powerful than FO on arbitrary structures and on finite ordered trees. It is also known that...

glutathione s-transferases (gsts) are members of multigenic family which have the essential functionin cells as an antioxidant. in the present study we studied the polymorphism of gstt1 and gstm1 deletion genotypes in iranian patients with primary closed angle glaucoma (pcag) compared to healthy subjects. we conducted a study of 41 pcag patients (24 women, 17 men) and 100 healthy participants (...