𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Generic Extensions and Generic Polynomials

✍ Scribed by Arne Ledet


Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
213 KB
Volume
30
Category
Article
ISSN
0747-7171

No coin nor oath required. For personal study only.

✦ Synopsis


We prove that the existence of generic polynomials and generic extensions are equivalent over an infinite field.


πŸ“œ SIMILAR VOLUMES


Generic Polynomials for Q8-, QC-, and QQ
✍ Arne Ledet πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 102 KB

We produce a description of Galois extensions with Galois group Q , QC, or 8 QQ, suitable for constructing generic polynomials.

Generic Polynomials with Few Parameters
✍ Gregor Kemper; Elena Mattig πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 335 KB

We call a polynomial g(t 1 , . . . , tm, X) over a field K generic for a group G if it has Galois group G as a polynomial in X, and if every Galois field extension N/L with K βŠ† L and Gal(N/L) ≀ G arises as the splitting field of a suitable specialization g(Ξ» 1 , . . . , Ξ»m, X) with Ξ» i ∈ L. We discu

Fragments of Martin's Maximum in generic
✍ Bernhard KΓΆnig; Yasuo Yoshinobu πŸ“‚ Article πŸ“… 2004 πŸ› John Wiley and Sons 🌐 English βš– 137 KB

## Abstract We show that large fragments of MM, e. g. the tree property and stationary reflection, are preserved by strongly (__Ο‰__~1~ + 1)‐game‐closed forcings. PFA can be destroyed by a strongly (__Ο‰__~1~ + 1)‐game‐closed forcing but not by an __Ο‰__~2~‐closed. (Β© 2004 WILEY‐VCH Verlag GmbH & Co.

Generic equivalents
✍ L A. Healey πŸ“‚ Article πŸ“… 1973 πŸ› John Wiley and Sons 🌐 English βš– 72 KB
Generic prescribing
✍ Michael R. Trimble πŸ“‚ Article πŸ“… 1987 πŸ› John Wiley and Sons 🌐 English βš– 189 KB
Galois Groups of Generalized Iterates of
✍ Shreeram S. Abhyankar; Ganapathy S. Sundaram πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 175 KB

Let q"pS'1 be a power of a prime p, and let k O be an over"eld of GF(q). Let m'0 be an integer, let J\* be a subset of +1, 2 , m,, and let E\* KO (>)"> qK # HZ( \* X H >O K\H where the X H are indeterminates. Let J ? be the set of all m! where is either 0 or a divisor of m di!erent from m. Let s(ΒΉ)"