✦ LIBER ✦
Substructure lattices and almost minimal end extensions of models of Peano arithmetic
✍ Scribed by James H. Schmerl
- Publisher
- John Wiley and Sons
- Year
- 2004
- Tongue
- English
- Weight
- 141 KB
- Volume
- 50
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
This paper concerns intermediate structure lattices Lt(𝒩/ℳ︁), where 𝒩 is an almost minimal elementary end extension of the model ℳ︁ of Peano Arithmetic. For the purposes of this abstract only, let us say that ℳ︁ attains L if L ≅ Lt(𝒩/ℳ︁) for some almost minimal elementary end extension of 𝒩. If T is a completion of PA and L is a finite lattice, then:
(A) If some model of T attains L, then every countable model of T does.
(B) If some rather classless, ℵ~1~‐saturated model of T attains L, then every model of T does. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)