On cuts in ultraproducts of linear orders I

2015/10/21 by Mohammad Golshani, Saharon Shelah, Golshani, Mohammad +1
Mathematics · #FOS: Mathematics #Logic (math.LO) #math.LO

paper · pdf · doi:10.48550/arxiv.1510.06278

published as J. Math. Log. 16 No. 2 (2016) 1650008, 34 · This is publication 1075 of second author

arxiv created 2016/09/17 · arxiv updated 2016/09/20

Abstract

For an ultrafilter D on a cardinal κ, we wonder for which pair (θ₁, θ₂) of regular cardinals, we have: for any (θ₁+θ₂)⁺-saturated dense linear order J, J^κ/ D has a cut of cofinality (θ₁, θ₂). We deal mainly with the case θ₁, θ₂ > 2^κ.

Related

• On cuts in ultraproducts of linear orders II
• On the number of cofinalities of cuts in ultraproducts of linear orders
• A connection between decomposability of ultrafilters and possible cofinalities
• Constructing regular ultrafilters from a model-theoretic point of view
• The combinatorics of reasonable ultrafilters