A note on the intuitionist fan theorem.

A note on spectral mapping theorem

This paper aims to present the well-known spectral mapping theorem for multi-variable functions.

A Zq-Fan theorem

In 1952, Ky Fan proved a combinatorial theorem generalizing the Borsuk-Ulam theorem stating that there is no Z2-equivariant map from the d-dimensional sphere S to the (d − 1)-dimensional sphere Sd−1. The aim of the present paper is to provide the same kind of combinatorial theorem for Dold's theorem, which is a generalization of the Borsuk-Ulam theorem when Z2 is replaced by Zq, and the spheres...

The fan theorem

A note on Pollard’s Theorem

Let A,B be nonempty subsets of a an abelian group G. Let Ni(A,B) denote the set of elements of G having i distinct decompositions as a product of an element of A and an element of B. We prove that ∑ 1≤i≤t |Ni(A,B)| ≥ t(|A|+ |B| − t− α+ 1 + w) − w, where α is the largest size of a coset contained in AB and w = min(α − 1, 1), with a strict inequality if α ≥ 3 and t ≥ 2, or if α ≥ 2 and t = 2. Thi...

A Note on Goodman's Theorem

Goodman's theorem states that intuitionistic arithmetic in all nite types plus full choice, HA ! + AC, is conservative over rst-order intuitionistic arithmetic HA. We show that this result does not extend to various subsystems of HA ! , HA with restricted induction.