A rigid Boolean algebra that admits the elimination of Q21

H. Mildenberg

Fundamenta Mathematicae (1993)

  • Volume: 142, Issue: 1, page 1-18
  • ISSN: 0016-2736

Abstract

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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 .

How to cite

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Mildenberg, H.. "A rigid Boolean algebra that admits the elimination of Q21." Fundamenta Mathematicae 142.1 (1993): 1-18. <http://eudml.org/doc/211970>.

@article{Mildenberg1993,
abstract = {Using ♢ , we construct a rigid atomless Boolean algebra that has no uncountable antichain and that admits the elimination of the Malitz quantifier $Q_1^2$.},
author = {Mildenberg, H.},
journal = {Fundamenta Mathematicae},
keywords = {homogeneous sets; diamond; elimination of Malitz quantifier; rigid atomless Boolean algebra; antichain},
language = {eng},
number = {1},
pages = {1-18},
title = {A rigid Boolean algebra that admits the elimination of Q21},
url = {http://eudml.org/doc/211970},
volume = {142},
year = {1993},
}

TY - JOUR
AU - Mildenberg, H.
TI - A rigid Boolean algebra that admits the elimination of Q21
JO - Fundamenta Mathematicae
PY - 1993
VL - 142
IS - 1
SP - 1
EP - 18
AB - Using ♢ , we construct a rigid atomless Boolean algebra that has no uncountable antichain and that admits the elimination of the Malitz quantifier $Q_1^2$.
LA - eng
KW - homogeneous sets; diamond; elimination of Malitz quantifier; rigid atomless Boolean algebra; antichain
UR - http://eudml.org/doc/211970
ER -

References

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  1. [Bal-Ku] J. Baldwin and D. W. Kueker, Ramsey quantifiers and the finite cover property, Pacific J. Math. 90 (1980), 11-19. Zbl0471.03022
  2. [Ba] J. E. Baumgartner, Chains and antichains in P (ω), J. Symbolic Logic 45 (1980), 85-92. 
  3. [Ba-Ko] J. E. Baumgartner and P. Komjáth, Boolean algebras in which every chain and antichain is countable, Fund. Math. 111 (1981), 125-133. Zbl0452.03044
  4. [Bü] G. Bürger, The ℒ < ω -theory of the class of Archimedian real closed fields, Arch. Math. Logic 28 (1989), 155-166. 
  5. [Ko] P. Koepke, On the elimination of Malitz quantifiers over archimedian real closed fields, ibid., 167-171. Zbl0693.03021
  6. [Mag-Mal] M. Magidor and J. Malitz, Compact extensions of L(Q) (part 1a), Ann. Math. Logic 11 (1977), 217-261. Zbl0356.02012
  7. [Mil] H. Mildenberger, Zur Homogenitätseigenschaft in Erweiterungslogiken, Dissertation, Freiburg 1990. 
  8. [Ot] M. Otto, Ehrenfeucht-Mostowski-Konstruktionen in Erweiterungslogiken, Dissertation, Freiburg 1990. 
  9. [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. Zbl0485.03011
  10. [Ru] M. Rubin, A Boolean algebra with few subalgebras, interval Boolean algebras and retractiveness, ibid. 278 (1983), 65-89. Zbl0524.06020
  11. [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. Zbl0472.03042

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