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Forcing in Finite Structures

✍ Scribed by Domenico Zambella

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
767 KB
Volume
43
Category
Article
ISSN
0044-3050

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✦ Synopsis

Abstract

We present a simple and completely model‐theoretical proof of a strengthening of a theorem of Ajtai: The independence of the pigeonhole principle from __I__Ξ”~0~(R). With regard to strength, the theorem proved here corresponds to the complexity/proof‐theoretical results of [10] and [14], but a different combinatorics is used. Techniques inspired by Razborov [11] replace those derived from HΓ₯stad [8]. This leads to a much shorter and very direct construction.

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