Saturation Properties of Ideals in Generic Extensions. I

DOI10.2307/1999861zbMath0485.03022OpenAlexW4247393197MaRDI QIDQ3944590

James E. Baumgartner, Alan D. Taylor

Publication date: 1982

Full work available at URL: https://doi.org/10.2307/1999861

zbMATH Keywords

Martin's axiomcovering propertyGCHcountable chain conditionsaturated idealsforcing with partial orderingsnegative preservation

Mathematics Subject Classification ID

Consistency and independence results (03E35) Large cardinals (03E55) Continuum hypothesis and Martin's axiom (03E50) Other combinatorial set theory (03E05)

Related Items (24)

Menas' conjecture and generic ultrapowers ⋮ Large cardinals and definable counterexamples to the continuum hypothesis ⋮ Rigid ideals ⋮ Potent Axioms ⋮ Strong downward Löwenheim-Skolem theorems for stationary logics. II: Reflection down to the continuum ⋮ In memoriam: James Earl Baumgartner (1943--2011) ⋮ MENAS’S CONJECTURE REVISITED ⋮ What makes the continuum ℵ₂ ⋮ Less saturated ideals ⋮ Calculating quotient algebras of generic embeddings ⋮ The extent of strength in the club filters ⋮ Splitting \({\mathcal P}_\kappa \lambda\) into maximally many stationary sets ⋮ On the size of closed unbounded sets ⋮ Local saturation of the non-stationary ideal over \(\mathcal P_{\kappa}\lambda\) ⋮ Collapsing \(\omega _2\) with semi-proper forcing ⋮ Forcing axioms and stationary sets ⋮ Two cardinal versions of diamond ⋮ Complete Quotient Boolean Algebras ⋮ On the structure of stationary sets ⋮ Game ideals ⋮ More game-theoretic properties of Boolean algebras ⋮ The nonstationary ideal and the other 𝜎-ideals on 𝜔₁ ⋮ Thin stationary sets and disjoint club sequences ⋮ On the weak distributivity game

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