Extending ω-consistent sets to maximally consistent, ω-complete sets
✍ Scribed by George Weaver; Michael Thau; Hugues Leblanc
- Publisher
- John Wiley and Sons
- Year
- 1990
- Tongue
- English
- Weight
- 168 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
✦ Synopsis
EXTENDING w-CONSISTENT SETS TO MAXIMALLY CONSISTENT, IN-COMPLETE SETS by GEORGE WEAVER in Bryn Mawr, Pennsylvania MICHAEL THAU and HUGUES LEBLANC in Philadelphia, Pennsylvania (U.S.A.) ')
Given L, a first order language, HENKIN'S completeness proof for L proceeds by showing that every consistent set of sentences in L can be extended to a maximally consistent and w-complete set. While every consistent set in L can be extended to a maximally consistent set in L, there are consistent sets which cannot be extended to a maximally consistent and w-complete set in L. In such cases, the extension is accomplished by introducing infinitely many new individual constants into the non-logical vocabulary of L. Here we show that even when L contains infinitely many individual constants there are w-consistent sets in L which cannot be extended to maximally consistent and w-complete sets in L.