Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
Using ♢ , we construct a rigid atomless Boolean algebra that has no uncountable antichain and that admits the elimination of the Malitz quantifier $Q_1^2$.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
1-18
Opis fizyczny
Daty
wydano
1993
otrzymano
1991-04-08
poprawiono
1991-07-24
poprawiono
1992-02-18
poprawiono
1992-09-14
Twórcy
autor
- Mathematisches Institut, Universität Bonn, Beringstr. 4, D-5300 Bonn 1, Germany
Bibliografia
- [Bal-Ku] J. Baldwin and D. W. Kueker, Ramsey quantifiers and the finite cover property, Pacific J. Math. 90 (1980), 11-19.
- [Ba] J. E. Baumgartner, Chains and antichains in P (ω), J. Symbolic Logic 45 (1980), 85-92.
- [Ba-Ko] J. E. Baumgartner and P. Komjáth, Boolean algebras in which every chain and antichain is countable, Fund. Math. 111 (1981), 125-133.
- [Bü] G. Bürger, The $ℒ^{<ω}$-theory of the class of Archimedian real closed fields, Arch. Math. Logic 28 (1989), 155-166.
- [Ko] P. Koepke, On the elimination of Malitz quantifiers over archimedian real closed fields, ibid., 167-171.
- [Mag-Mal] M. Magidor and J. Malitz, Compact extensions of L(Q) (part 1a), Ann. Math. Logic 11 (1977), 217-261.
- [Mil] H. Mildenberger, Zur Homogenitätseigenschaft in Erweiterungslogiken, Dissertation, Freiburg 1990.
- [Ot] M. Otto, Ehrenfeucht-Mostowski-Konstruktionen in Erweiterungslogiken, Dissertation, Freiburg 1990.
- [Ro-Tu] P. Rothmaler and P. Tuschik, A two cardinal theorem for homogeneous sets and the elimination of Malitz quantifiers, Trans. Amer. Math. Soc. 269 (1982), 273-283.
- [Ru] M. Rubin, A Boolean algebra with few subalgebras, interval Boolean algebras and retractiveness, ibid. 278 (1983), 65-89.
- [Sh] S. Shelah, On uncountable Boolean algebras with no uncountable pairwise comparable or incomparable sets of elements, Notre Dame J. Formal Logic 22 (1981), 301-308.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv142i1p1bwm