Hierarchies of constructible sets

Generalisations of Gödel’s universe of constructible sets

Computing the Canonical Representation of Constructible Sets

In the basic paper defining the Gröbner Cover [16] for discussing parametric polynomial systems of equations, we 8 introduced algorithms that have been improved since then. We used our own algorithm buildtree for computing 9 the initial Comprehensive Gröbner System (CGS), needed for the Gröbner Cover, now substituted in the Singular [7] 10 library “grobcov.lib” by themore efficientKapur–Sun–Wan...

Computing with Constructible Sets in Maple

Constructible sets are the geometrical objects naturally attached to triangular decompositions, as polynomial ideals are the algebraic concept underlying the computation of Gröbner bases. This relation becomes even more complex and essential in the case of polynomial systems with infinitely many solutions. In this paper, we introduce ConstructibleSetTools a new module of the RegularChains libra...

The Complexity of Local Dimensions for Constructible Sets

We show that deciding whether an algebraic variety has an irreducible component of codimension at least d is an NP C-complete problem for every xed d (and is in the Arthur-Merlin class if we assume a bit model of computation). However, when d is not xed but is instead part of the input, we show that the problem is not likely to be in NP C or in coNP C. These results are generalized to arbitrary...

Reals constructible from many countable sets of ordinals

We show that if there exist proper class many Woodin cardinals, then the set of reals x for which there is exists an ordinal α with {a ∈ Pω1(α) | x ∈ L[a]} stationary is countable. These results were announced in [2]. Given a real x and an ordinal α, we let C(x, α) denote the set {a ∈ Pω1(α) | x ∈ L[a]}. We let C denote the set of reals x for which there exists an ordinal α such that C(x, α) is...