7,677 research outputs found
On structures in hypergraphs of models of a theory
We define and study structural properties of hypergraphs of models of a
theory including lattice ones. Characterizations for the lattice properties of
hypergraphs of models of a theory, as well as for structures on sets of
isomorphism types of models of a theory, are given
The complexity of the list homomorphism problem for graphs
We completely classify the computational complexity of the list H-colouring
problem for graphs (with possible loops) in combinatorial and algebraic terms:
for every graph H the problem is either NP-complete, NL-complete, L-complete or
is first-order definable; descriptive complexity equivalents are given as well
via Datalog and its fragments. Our algebraic characterisations match important
conjectures in the study of constraint satisfaction problems.Comment: 12 pages, STACS 201
On function field Mordell-Lang and Manin-Mumford
We present a reduction of the function field Mordell-Lang conjecture to the
function field Manin-Mumford conjecture, in all characteristics, via model
theory, but avoiding recourse to the dichotomy theorems for (generalized)
Zariski structures.
In this version 2, the quantifier elimination result in positive
characteristic is extended from simple abelian varieties to all abelian
varieties, completing the main theorem in the positive characteristic case.
In version 3, some corrections are made to the proof of quantifier
elimination in positive characteristic, and the paper is substantially
reorganized.Comment: 21 page
On a Glimm -- Effros dichotomy theorem for Souslin relations in generic universes
We prove that if every real belongs to a set generic extension of the
constructible universe then every \Sigma_1^1 equivalence E on reals either
admits a Delta_1^HC reduction to the equality on the set 2^{<\om_1} of all
countable binary sequences, or continuously embeds E_0, the Vitali equivalence.
The proofs are based on a topology generated by OD sets
On effective sigma-boundedness and sigma-compactness
We prove several theorems on sigma-bounded and sigma-compact pointsets. We
start with a known theorem by Kechris, saying that any lightface \Sigma^1_1 set
of the Baire space either is effectively sigma-bounded (that is, covered by a
countable union of compact lightface \Delta^1_1 sets), or contains a
superperfect subset (and then the set is not sigma-bounded, of course). We add
different generalizations of this result, in particular, 1) such that the
boundedness property involved includes covering by compact sets and equivalence
classes of a given finite collection of lightface \Delta^1_1 equivalence
relations, 2) generalizations to lightface \Sigma^1_2 sets, 3) generalizations
true in the Solovay model.
As for effective sigma-compactness, we start with a theorem by Louveau,
saying that any lightface \Delta^1_1 set of the Baire space either is
effectively sigma-compact (that is, is equal to a countable union of compact
lightface \Delta^1_1 sets), or it contains a relatively closed superperfect
subset. Then we prove a generalization of this result to lightface \Sigma^1_1
sets.Comment: arXiv admin note: substantial text overlap with arXiv:1103.106
- …