# A rigid Boolean algebra that admits the elimination of Q21

Fundamenta Mathematicae (1993)

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

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topMildenberg, 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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- [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
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- [Ko] P. Koepke, On the elimination of Malitz quantifiers over archimedian real closed fields, ibid., 167-171. Zbl0693.03021
- [Mag-Mal] M. Magidor and J. Malitz, Compact extensions of L(Q) (part 1a), Ann. Math. Logic 11 (1977), 217-261. Zbl0356.02012
- [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. Zbl0485.03011
- [Ru] M. Rubin, A Boolean algebra with few subalgebras, interval Boolean algebras and retractiveness, ibid. 278 (1983), 65-89. Zbl0524.06020
- [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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