Some Weak Variants of the Existence and Disjunction Properties in Intermediate Predicate Logics

We discuss relationships among the existence property, the disjunction property, and their weak variants in the setting of intermediate predicate logics. We deal with the weak and sentential existence properties, and the Z-normality, which is a weak variant of the disjunction property. These weak variants were presented in the author’s previous paper [16]. In the present paper, the Kripke sheaf semantics is used.

Real hypersurfaces in complex two-plane Grassmannians with recurrent Ricci tensor

In this paper, we have introduced a new notion of generalized Tanaka–Webster Reeb recurrent Ricci tensor of real hypersurfaces in complex two-plane Grassmannians G2(ℂm+2). Next, we show a non-existence property for real hypersurfaces M in G2(ℂm+2) with such a curvature condition.

The disjunction and related properties for constructive Zermelo-Fraenkel set theory

This paper proves that the disjunction property, the numerical existence property. Church's rule, and several other metamathematical properties hold true for Constructive Zermelo-Fraenkel Set Theory, CZF, and also for the theory CZF augmented by the Regular Extension Axiom.As regards the proof technique, it features a self-validating semantics for CZF that combines realizability for extensional set theory and truth.