2015/11/14 by Ali Sadegh Daghighi, Daghighi, Ali Sadegh, Massoud Pourmahdian +1
Mathematics · #FOS: Mathematics #Logic (math.LO) #math.LO
paper · pdf · doi:10.48550/arxiv.1511.04598
arxiv created 2015/11/21 · arxiv updated 2015/11/24
It is proved that the consistency strength of having definable tree property for successors of all regular cardinals is the consistency strength of having proper class many small large cardinals which are defined very similar to indescribables but are much weaker in consistency strength. Also the consistency strength of definable tree property for successor of a singular cardinal is reduced to the existence of a supercompact cardinal and a measurable above it.