Some remarks on Hausdorff gaps and automorphisms of P(ω)/fin

Magdalena Grzech


We present, under the Continuum Hypothesis (CH), a construction of an automorphism of P(ω)/fin which maps a Hausdorff gap onto increasingly ordered gap of type (w1, w1) which is not a Hausdorff gap.

Słowa kluczowe: compactification, automorphism, Boolean algebra

F Hausdorff Summen von Mengen, F. Mengen, Fund. Math. 26, 1936, 241-255

Rudin W., Homogenity problems in the theory of Čech compactification, Duke Math. Journal 23, 1956, 409-419.

Shelah S., Proper Forcing, Lecture Notes in Mathematics 940, Springer Verlag, Berlin 1982.

Steprans J., Shelah S., PFA implies all automorphisms are trivial, Proc. Amer. Math. Soc. vol. 104, no. 4, 1988, 1220-1225.

Sikorski R., On an analogy between measures and homomorphisms, Ann. Soc. Pol. Math. 23, 1950, 1-20.

Sikorski R., Boolean Algebras, Sprnger-Verlag, Berlin 1969.

Velickovic B., OCA and automorphisms of P(ω)/fin Topology and its Applications, vol. 49, 1993, 1-13.