Fréchet Borel ideals with Borel orthogonal

Ideals with bases of unbounded Borel complexity

We present several naturally defined σ–ideals which have Borel bases but, unlike for the classical examples, these bases are not of bounded Borel complexity. We investigate set-theoretic properties of such σ–ideals.

Borel Ideals in Three Variables

i=1 gijXi, g = (gij) ∈ Gl(n,k)), given any term-ordering< and homogeneous ideal a ⊆ P(n), there exists a non-empty open subset U of Gl(n,k) such that as g ranges in U, gin(a) := in(g(a)) is constant. Moreover, gin(a) is fixed by the group B of upper-triangular invertible matrices, if X1 > · · · > Xn, while gin(a) is fixed by the group B′ of lower-triangular invertible matrices if X1 < · · · < X...

Borel homomorphisms of smooth σ-ideals

Given a countable Borel equivalence relation E on a Polish space, let IE denote the σ-ideal generated by the Borel partial transversals of E. We show that there is a Borel homomorphism from IE to IF if and only if there is a smooth-to-one Borel homomorphism from a finite index Borel subequivalence relation of E to F . As a corollary, we see that IE is homogeneous in the sense of Zapletal (2007,...

ON SPECIAL p-BOREL FIXED IDEALS

We define the reduced horseshoe resolution and the notion of conjoined pairs of ideals in order to study the minimal graded free resolution of a class of p-Borel ideals and recover Pardue’s regularity formula for them. It will follow from our technique that the graded betti numbers of these ideals do not depend on the characteristic of the base field k.

Borel-fixed Ideals and Reduction Number