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Pseudo-trees and Boolean algebras

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Abstract

We consider Boolean algebras constructed from pseudo-trees in various ways and make comments about related classes of Boolean algebras.

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References

  1. M. G.Bell and J.Pelant (1987) Continuous images of compact semilattices,Canad. Math. Bull. 30(1), 109–113.

    Google Scholar 

  2. R. Bonnet (1991) Superatomic subalgebras of an interval algebra, preprint no. 91-001 Universität Bielefeld.

  3. R.Bonnet and S.Shelah (1985) Narrow Boolean algebras,Annals Pure Applied Logic 28, 1–12.

    Google Scholar 

  4. G. Brenner (1982) Tree algebras, Ph.D. dissertation, University of Colorado, 82 pp.

  5. G.Brenner (1983) A simple construction for rigid and weakly homogeneous Boolean algebras answering a question of Rubin,Proc. Amer. Math. Soc. 87, 601–606.

    Google Scholar 

  6. G.Brenner and J. D.Monk (1983) Tree algebras and chains,Springer Lecture Notes in Mathematics 1004, 54–66.

    Google Scholar 

  7. G.Chertnov (1985) Compacta that are coabsolute with linearly ordered ones,Sib. Math. J. 26, 765–776.

    Google Scholar 

  8. E. van Douwen, Small tree algebras with nontree subalgebras, preprint extracted from handwritten notes by J. van Mill.

  9. K.Eda (1975) Some properties of tree algebras,Comment. Math. Univ. St. Pauli 24(1), 1–5.

    Google Scholar 

  10. E.Evans (1980) Slim trees,J. Austral. Math. Soc. (Series A) 30, 201–214.

    Google Scholar 

  11. L.Heindorf (1990) Boolean semigroup rings and exponentials of compact zero-dimensional spaces,Fund Math. 135, 37–47.

    Google Scholar 

  12. L.Heindorf (1991) Chains in Boolean semigroup algebras,Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 37(1), 93–96.

    Google Scholar 

  13. T. Jech (1978)Set Theory, Acad. Press.

  14. S.Koppelberg (1973) Injective hulls of chains,Arch. der Math. 24(3), 225–229.

    Google Scholar 

  15. S.Koppelberg (1977) Boolean algebras as unions of chains of subalgebras,Alg. Univ. 7, 195–203.

    Google Scholar 

  16. S.Koppelberg (1988) Counterexamples in minimally generated Boolean algebras,Acta Univ. Carolinae—Math. et Physica 29(2), 27–36.

    Google Scholar 

  17. S. Koppelberg (1989)General Theory of Boolean Algebras. Handbook of Boolean Algebras, Part I, North Holland.

  18. S.Koppelberg (1989) Minimally generated Boolean algebras,Order 5, 393–406.

    Google Scholar 

  19. J. D.Monk (1984) Cardinal functions on Boolean algebras,Annals of Discr. Math. 23, 9–37.

    Google Scholar 

  20. M.Rubin (1983) A Boolean algebra with few subalgebras, interval Boolean algebras and retractiveness,Trans. Amer. Math. Soc. 278(1), 65–89.

    Google Scholar 

  21. R. Sikorski (1964)Boolean Algebras, Second edition, Springer Verlag.

  22. S.Williams (1982) Trees, Gleason spaces, and coabsolutes of βN\N, Trans. Amer. Math. Soc. 271(1), 83–100.

    Google Scholar 

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Communicated by B. Jónsson

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Koppelberg, S., Monk, J.D. Pseudo-trees and Boolean algebras. Order 8, 359–374 (1991). https://doi.org/10.1007/BF00571186

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