H is the theory extending β-conversion by identifying all closed unsolvables. Hω is the closure of this theory under the ω-rule (and β-conversion). A long-standing conjecture of H. Barendregt states that the provable equations of Hω form a Π11-complete set. Here we prove that conjecture.

In the present paper, by considering the notion of MV-modules which is the structure that naturally correspond to lu-modules over lu-rings, we prove some results on prime A-ideals and state some conditions to obtain a prime A-ideal in MV-modules. Also, we state some conditions that an A-ideal is not prime and investigate conditions that $Ksubseteq bigcup _{i=1}^{n}K_{i}$ implies $Ksubseteq K_{j...

‎there are a few finite groups that are determined up to isomorphism solely by their order, such as $mathbb{z}_{2}$ or $mathbb{z}_{15}$. still other finite groups are determined by their order together with other data, such as the number of elements of each order, the structure of the prime graph, the number of order components, the number of sylow $p$-subgroups for each prime $p$, etc. in this...

‎There are a few finite groups that are determined up to isomorphism solely by their order, such as $mathbb{Z}_{2}$ or $mathbb{Z}_{15}$. Still other finite groups are determined by their order together with other data, such as the number of elements of each order, the structure of the prime graph, the number of order components, the number of Sylow $p$-subgroups for each prime $p$, etc. In this...

We investigate the theory IAo + Q, and strengthen [Bu86. Theorem 8.6] to the following: if NP 7 co-NP. then 1-completeness for witness comparison foumulas is not provable in bounded arithmetic.

In this paper we study the local behavior of a solution to the Lamé system with Lipschitz coefficients in dimension n ≥ 2. Our main result is the bound on the vanishing order of a nontrivial solution, which immediately implies the strong unique continuation property. This paper solves the open problem of the strong uniqueness continuation property for the Lamé system with Lipschitz coefficients...