By Ehud Hrushovski
Read or Download [Article] Computing Galois group of a linear differential equation PDF
Similar logic books
This publication brings jointly philosophers, mathematicians and logicians to penetrate very important difficulties within the philosophy and foundations of arithmetic. In philosophy, one has been fascinated by the competition among constructivism and classical arithmetic and different ontological and epistemological perspectives which are mirrored during this competition.
The improvement of latest and more advantageous evidence platforms, facts codecs and facts seek tools is among the so much crucial objectives of good judgment. yet what's an evidence? What makes an evidence greater than one other? How can an explanation be discovered successfully? How can an evidence be used? Logicians from various groups often supply significantly varied solutions to such questions.
- The Rise of Modern Logic: from Leibniz to Frege (Handbook of the History of Logic, Volume 3)
- Logic Colloquium ’03: Proceedings of the Annual European Summer
- Logic and Programming
- Quanta, logic and spacetime
- storia della logica
- Truth, syntax and modality: Proceedings Philadelphia, 1970
Extra resources for [Article] Computing Galois group of a linear differential equation
Complement: Galois theory of ω-constructible sets. The definability theorem B1 presented above is somewhat weaker than the original presentation, as only constructible sets are allowed. We present here another version that permits also ωconstructible sets. We require stable embeddedness, but still very far from a global stability assumption. 1! Moreover, it is natural to work in an arbitrary universal domain for a universal theory T0 , not necessarily having a comprehensible completion. So we no longer assume QE (cf.
It 130 E. HRUSHOVSKI is stable so that every definable set (indeed every set) is stably embedded. C = C˜ is the equation Dx = 0. Q is the solution set to a linear differential equation. The torsor P in that case can be taken to be orbit of Aut(U/F, C) on the set of bases, an open subset of Qn ; the opposite group is the subgroup of elements Mn (C) preserving P and the action of Aut(U/F, C) on P , where Mn (C) is the group of n × n matrices with coefficients from C, acting on V n by matrix-vector multiplication.
Let D ⊂ U be Σ-constructible. Then Aut(U/D)-conjugacy is an ω-constructible equivalence relation. Proof. 1, we may assume D is stably embedded. In this case, two elements a, b are Aut(U/D)-conjugate iff for any constructible R and any tuple c of elements of D, one has R(a, c) ≡ R(b, c). This shows immediately that Aut(U/D)-conjugacy is ω-constructible. ω-constructible groups. Finally, we will mention without proof some background facts regarding definability of groups. By an ω-constructible group we mean a group whose universe is an ω-constructible set, and whose operations are constructible maps (maps whose graphs are constructible).
[Article] Computing Galois group of a linear differential equation by Ehud Hrushovski