Singularizing successor cardinals by forcing
نویسندگان
چکیده
منابع مشابه
Partition Relations for Successor Cardinals
This paper investigates the relations K+ --t (a): and its variants for uncountable cardinals K. First of all, the extensive literature in this area is reviewed. Then, some possibilities afforded by large cardinal hypotheses are derived, for example, if K is measurable, then K + + (K + K + 1, a): for every a < K +. Finally, the limitations imposed on provability in ZFC by L and by relative consi...
متن کاملLarge Cardinals with Forcing
This chapter describes, following the historical development, the investigation of large cardinal hypotheses using the method of forcing. Large cardinal hypotheses, also regarded as strong axioms of infinity, have stimulated a vast mainstream of modern set theory, and William Mitchell’s chapter in this volume deals with their investigation through inner models, Menachem Kojman’s chapter with th...
متن کاملSuccessor Large Cardinals in Symmetric Extensions ∗
We give an exposition in modern language (and using partial orders) of Jech’s method for obtaining models where successor cardinals have large cardinal properties. In such models, the axiom of choice must necessarily fail. In particular, we show how, given any regular cardinal and a large cardinal of the requisite type above it, there is a symmetric extension of the universe in which the axiom ...
متن کاملProper forcing and remarkable cardinals
The present paper investigates the power of proper forcings to change the shape of the universe, in a certain well-defined respect. It turns out that the ranking among large cardinals can be used as a measure for that power. However, in order to establish the final result I had to isolate a new large cardinal concept, which I dubbed “remarkability.” Let us approach the exact formulation of the ...
متن کاملA minimal Prikry-type forcing for singularizing a measurable cardinal
Recently, Gitik, Kanovei and the first author proved that for a classical Prikry forcing extension the family of the intermediate models can be parametrized by Pp!q{finite. By modifying the standard Prikry tree forcing we define a Prikry-type forcing which also singularizes a measurable cardinal but which is minimal, i.e. there are no intermediate models properly between the ground model and th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2017
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/13784