✦ LIBER ✦

A note on the Σ1 collection scheme and fragments of bounded arithmetic

✍ Scribed by Zofia Adamowicz; Leszek Aleksander Kołodziejczyk

Publisher: John Wiley and Sons
Year: 2010
Tongue: English
Weight: 115 KB
Volume: 56
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200810043

No coin nor oath required. For personal study only.

✦ Synopsis

Bounded arithmetic, collection principle, weak pigeonhole principle.

MSC (2000) 03F30

We show that for each n ≥ 1, if T n 2 does not prove the weak pigeonhole principle for Σ b n functions, then the collection scheme BΣ1 is not finitely axiomatizable over T n 2 . The same result holds with S n 2 in place of T n 2 .

📜 SIMILAR VOLUMES

A note on effective ultrapowers: Uniform

A note on effective ultrapowers: Uniform failure of bounded collection

✍ Thomas McLaughlin 📂 Article 📅 1993 🏛 John Wiley and Sons 🌐 English ⚖ 302 KB

## Abstract By suitably adapting an argument of Hirschfeld (see [2, Chapter 9]), we show that there is a single Δ~1~ formula that defeats “bounded collection” for any model of II~2~ Arithmetic that is either a recursive ultrapower or an existentially complete model. Some related facts are noted. MS

Studies on Synthesis of the C-1 to C-18

Studies on Synthesis of the C-1 to C-18 Fragment of Pamamycins 607 and 621A

✍ Guobao Ren; Yikang Wu 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 131 KB 👁 1 views

A Note on the Photosensitivity of Phenot

A Note on the Photosensitivity of Phenothiazine Derivatives * *Research and Development Division of Smith Kline and French Laboratories, Philadelphia 1, Pa.

✍ Ravin, Louis J. ;Kennon, Lloyd ;Swintosky, Joseph V. 📂 Article 📅 1958 🏛 Elsevier ⚖ 94 KB 👁 1 views

Vitamins B1. A note on the stability of

Vitamins B1. A note on the stability of thiamine hydrochloride in aqueous solution in the presence of iodine and potassium iodide

✍ Murphy, Hubert W. ;Goodyear, Ohn M. 📂 Article 📅 1949 🏛 Elsevier ⚖ 199 KB 👁 2 views

Carbon–Nitrogen Bond Formation by the Re

Carbon–Nitrogen Bond Formation by the Reaction of 1,2-Cumulenes with a Ditantalum Complex Containing Side-On- and End-On-Bound Dinitrogen

✍ Dr. Joachim Ballmann; Alyssa Yeo; Dr. Brian O. Patrick; Prof. Dr. Michael D. Fry 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 306 KB 👁 2 views

Scheme 1. Reactivity of 1 towards CÀC double and triple bonds.

Carbon–Nitrogen Bond Formation by the Re

Carbon–Nitrogen Bond Formation by the Reaction of 1,2-Cumulenes with a Ditantalum Complex Containing Side-On- and End-On-Bound Dinitrogen

✍ Dr. Joachim Ballmann; Alyssa Yeo; Dr. Brian O. Patrick; Prof. Dr. Michael D. Fry 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 317 KB 👁 2 views