Strong sequences and partition relations
Keywords:
Strong sequences, Erdös-Rado theorem, partition relations, inaccessible cardinals, singular cardinalsAbstract
The first result in partition relations topic belongs to Ramsey (1930). Since that this topic has been still explored. Probably the most famous partition theorem is Erdös-Rado theorem (1956). On the other hand in 60’s of the last century Efimov introduced strong sequences method, which was used for proving some famous theorems in dyadic spaces. The aim of this paper is to generalize theorem on strong sequences and to show that it is equivalent to generalized version of well-known Erdös-Rado theorem. It will be also shown that this equivalence holds for singulars. Some applications and conclusions will be presented too.
References
Baumgartner, James E., Alan D. Taylor, and Stanley Wagon. Structural properties of ideals. Vol. 197 of Dissertationes Math. (Rozprawy Mat.). Warszawa: PWN–Polish Scientific Publishers, 1982.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Comfort, W. Wistar, and Stylianos A. Negrepontis. Chain conditions in topology. Vol. 79 of Cambridge Tracts in Mathematics. Cambridge-New York: Cambridge University Press, 1982.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Efimov, B. A. “Dyadic bicompacta.” (Russian) Trudy Moskov. Mat. Obšč. 14 (1965): 211–247.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Engelking, Ryszard. General topology. Vol. 60 of Monografie Matematyczne. Warszawa: PWN–Polish Scientific Publishers, 1977.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Erdös, Paul, and Richard Rado. “A partition calculus in set theory.” Bull. Amer. Math. Soc. 62 (1956): 427–489.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Hajnal, András. “Proof of a conjecture of S. Ruziewicz.” Fund. Math. 50 (1961/1962): 123–128.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Jech, Thomas. Set theory. New York-London: Academic Press, 1978.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Jureczko, Joanna. “On inequalities among some cardinal invariants.” Math. Aeterna 6, no. 1 (2016): 87–98.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Jureczko, Joanna. “Strong sequences and independent sets.” Math. Aeterna 6, no. 2 (2016): 141–152.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Jureczko, Joanna. “k-strong sequences and the existence of generalized independent families.” Open Mathematics (2017), to appear.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Szpilrajn, Edward. “Remarque sur les produits cartésiens d’espaces topologiques.” C. R. (Doklady) Acad. Sci. URSS (N. S.) 31 (1941): 525–527.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Turzański, Marian. “Strong sequences and the weight of regular spaces.” Comment. Math. Univ. Carolin. 33, no. 3 (1992): 557–561.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Turzański, Marian. “On the selector of twin functions.” Comment. Math. Univ. Carolin. 39, no. 2 (1998): 303–307.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
