Switch to: References

Add citations

You must login to add citations.
  1. In memoriam: James Earl Baumgartner (1943–2011).J. A. Larson - 2017 - Archive for Mathematical Logic 56 (7):877-909.
    James Earl Baumgartner (March 23, 1943–December 28, 2011) came of age mathematically during the emergence of forcing as a fundamental technique of set theory, and his seminal research changed the way set theory is done. He made fundamental contributions to the development of forcing, to our understanding of uncountable orders, to the partition calculus, and to large cardinals and their ideals. He promulgated the use of logic such as absoluteness and elementary submodels to solve problems in set theory, he applied (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Forcing with adequate sets of models as side conditions.John Krueger - 2017 - Mathematical Logic Quarterly 63 (1-2):124-149.
    We present a general framework for forcing on ω2 with finite conditions using countable models as side conditions. This framework is based on a method of comparing countable models as being membership related up to a large initial segment. We give several examples of this type of forcing, including adding a function on ω2, adding a nonreflecting stationary subset of, and adding an ω1‐Kurepa tree.
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  • Coherent adequate forcing and preserving CH.John Krueger & Miguel Angel Mota - 2015 - Journal of Mathematical Logic 15 (2):1550005.
    We develop a general framework for forcing with coherent adequate sets on [Formula: see text] as side conditions, where [Formula: see text] is a cardinal of uncountable cofinality. We describe a class of forcing posets which we call coherent adequate type forcings. The main theorem of the paper is that any coherent adequate type forcing preserves CH. We show that there exists a forcing poset for adding a club subset of [Formula: see text] with finite conditions while preserving CH, solving (...)
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  • Mitchell's theorem revisited.Thomas Gilton & John Krueger - 2017 - Annals of Pure and Applied Logic 168 (5):922-1016.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Quotients of strongly proper forcings and guessing models.Sean Cox & John Krueger - 2016 - Journal of Symbolic Logic 81 (1):264-283.
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  • Absoluteness via resurrection.Giorgio Audrito & Matteo Viale - 2017 - Journal of Mathematical Logic 17 (2):1750005.
    The resurrection axioms are forcing axioms introduced recently by Hamkins and Johnstone, developing on ideas of Chalons and Veličković. We introduce a stronger form of resurrection axioms for a class of forcings Γ and a given ordinal α), and show that RAω implies generic absoluteness for the first-order theory of Hγ+ with respect to forcings in Γ preserving the axiom, where γ = γΓ is a cardinal which depends on Γ. We also prove that the consistency strength of these axioms (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations