𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On Σ1-definable Functions Provably Total in I ∏

✍ Scribed by Teresa Bigorajska

Publisher
John Wiley and Sons
Year
1995
Tongue
English
Weight
159 KB
Volume
41
Category
Article
ISSN
0044-3050

No coin nor oath required. For personal study only.

✦ Synopsis

We prove the following theorem: Let cp(z) be a formula in the language of the theory PAof discretely ordered commutative rings with unit of the form 3 y p ' ( z , y ) with 'p' E Ao and let f, : N -+ R be such that f,(z) = y iff cp'(z, y) & (Vz < y) ~( p ' ( z , 2 ) . If ITIF I -(Vz 2 0) cp(z), then there exists a natural number K such that I t -3yt/z(z > y + f,+,(z) < zK). Here In, denotes the theory PAplus the scheme of induction for formulas ~( z ) of the form Vy'cp'(z,y') with p' E A,.

📜 SIMILAR VOLUMES

Continuous Functions on Totally Ordered
Continuous Functions on Totally Ordered Spaces That Are Compact in Their Order Topologies
✍ R.G. Haydon; J.E. Jayne; I. Namioka; C.A. Rogers 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 283 KB

The totally ordered spaces that are compact and connected in their order topologies are characterized as images of lexicographic cubes. The Banach space of continuous functions on the lexicographic product of compact totally ordered spaces, whose spaces of continuous functions have locally uniformly

On a class of extremal solutions of a mo
On a class of extremal solutions of a moment problem for rational matrix-valued functions in the nondegenerate case I
✍ Bernd Fritzsche; Bernd Kirstein; Andreas Lasarow 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 284 KB 👁 1 views

## Abstract The main theme of this paper is the discussion of a parametrized family of solutions of a finite moment problem for rational matrix‐valued functions in the nondegenerate case. We will show that each member of this family is extremal in several directions concerning some point of the ope