Article

Full entry | PDF   (0.2 MB)
Keywords:
Open Coloring Axiom; dense sets of reals; towers; forcing; Suslin trees
Summary:
We shall show that Open Coloring Axiom has different influence on the algebra \$\Cal P(\Bbb N)/fin\$ than on \$\Bbb N^\Bbb N/fin\$. The tool used to accomplish this is forcing with a Suslin tree.
References:
[1] Abraham U., Rubin M., Shelah S.: On the consistency of some partition theorems for continuous colorings, and the structure of \$\aleph_1\$-dense real order types. Ann. of Pure and Appl. Logic 29 (1985), 123-206. MR 0801036
[2] Baumgartner J.: All \$\aleph_1\$-dense sets of reals can be isomorphic. Fundamenta Mathematicae 79 (1973), 100-106. MR 0317934 | Zbl 0274.02037
[3] Devlin K., Johnsbråten H.: The Souslin Problem. Springer Lecture Notes in Mathematics, # 405 (1974). MR 0384542
[4] Dordal P.L.: Towers in \$[ømega]^ømega\$ and \$^ømegaømega\$. Ann. of Pure and Appl. Logic 247-277 (1989), 45.3. MR 1032832
[5] Fremlin D.: Consequences of Martin's Axiom. Cambridge University Press (1984). Zbl 0551.03033
[6] Gruenhage G.: Cosmicity of cometrizable spaces. Trans. AMS 313 (1989), 301-315. MR 0992600 | Zbl 0667.54012
[7] Todorčević S.: Partition Problems in Topology. AMS Providence, Rhode Island (1989). MR 0980949
[8] Todorčević S.: Oscillations of sets of integers. to appear. MR 1601383
[9] Veličković B.: OCA and automorphisms of \$\Cal P(ømega)/fin\$. Topology Appl. 49 (1993), 1-13. MR 1202874
[10] Weese M.: personal communication.

Partner of