%0 Generic %1 citeulike:71358 %A Halbeisen, L. %A Shelah, S. %D 1994 %K arithmetic set theory %T Consequences of arithmetic for set theory %U http://citeseer.ist.psu.edu/halbeisen94consequences.html %X In this paper, we consider certain cardinals in ZF #set theory without AC, the Axiom of Choice#. In ZFC #set theory with AC#, given any cardinals C and D; either C # D or D # C: However, in ZF this is no longer so. For a given in#nite set A consider seq 1 1 #A#, the set of all sequences of A without repetition. We compare seq 1 1 #A# , the cardinality of this set, to P#A# , the cardinality of the power set of A. What is provable about these two cardinals in ZF? The main result of this...

@misc{citeulike:71358, abstract = {In this paper, we consider certain cardinals in ZF #set theory without AC, the Axiom of Choice#. In ZFC #set theory with AC#, given any cardinals C and D; either C # D or D # C: However, in ZF this is no longer so. For a given in#nite set A consider seq 1 1 #A#, the set of all sequences of A without repetition. We compare seq 1 1 #A# , the cardinality of this set, to P#A# , the cardinality of the power set of A. What is provable about these two cardinals in ZF? The main result of this...}, added-at = {2007-08-18T13:22:24.000+0200}, author = {Halbeisen, L. and Shelah, S.}, biburl = {https://www.bibsonomy.org/bibtex/2e9dcfae60bb908e164ba95c4805d0779/a_olympia}, citeulike-article-id = {71358}, description = {citeulike}, interhash = {28979e97ba4e415179e2dd2879b77d32}, intrahash = {e9dcfae60bb908e164ba95c4805d0779}, keywords = {arithmetic set theory}, priority = {4}, timestamp = {2007-08-18T13:22:58.000+0200}, title = {Consequences of arithmetic for set theory}, url = {http://citeseer.ist.psu.edu/halbeisen94consequences.html}, year = 1994 }