Topics in set theory. Lebesgue measurability, large cardinals, forcing axioms, rho-functions

Publication date: 18 September 1992

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

partitions trees Martin's axiom inaccessible cardinal supercompact cardinal forcing axioms partition relations minimal walks saturated ideals measurable sets of reals in L[${\mathbb{R}}$]non-Lebesgue measurable sets of reals square sequences uncountable homogeneous set

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations (03-02) Consistency and independence results (03E35) Large cardinals (03E55) Other combinatorial set theory (03E05) Other set-theoretic hypotheses and axioms (03E65)

Related Items (37)

Partition relations for $\kappa$-normal ideals on $P_{\kappa}(\lambda)$ ⋮ Simultaneously vanishing higher derived limits without large cardinals ⋮ PFA(S) and automorphisms of $\mathcal{P}(\mathbb{N}) / \mathrm{fin}$ ⋮ Proper and piecewise proper families of reals ⋮ Some remarks on the open coloring axiom ⋮ $\text{PFA}(S)[S$ for the masses] ⋮ Two chain conditions and their Todorčević's fragments of Martin's axiom ⋮ The relative strengths of fragments of Martin's axiom ⋮ What makes the continuum ℵ₂ ⋮ Random forcing and (S) and (L). ⋮ THE DIAGONAL STRONG REFLECTION PRINCIPLE AND ITS FRAGMENTS ⋮ An undecidable extension of Morley's theorem on the number of countable models ⋮ Absoluteness via resurrection ⋮ Subcomplete forcing principles and definable well‐orders ⋮ Local weak presaturation of the strongly non‐stationary ideal ⋮ A non-implication between fragments of Martin's axiom related to a property which comes from Aronszajn trees ⋮ A universal continuum of weight $\aleph $ ⋮ SET MAPPING REFLECTION ⋮ Hierarchies of forcing axioms I ⋮ Coherent sequences and threads ⋮ Why Y-c.c. ⋮ Bounding the consistency strength of a five element linear basis ⋮ An Asplund space with norming Markuševič basis that is not weakly compactly generated ⋮ Canonical fragments of the strong reflection principle ⋮ A consistency result on thin-very tall Boolean algebras ⋮ Bounded forcing axioms and the continuum ⋮ Reflection and Weakly Collectionwise Hausdorff Spaces ⋮ On the structure of stationary sets ⋮ Stacking mice ⋮ Forcing the mapping reflection principle by finite approximations ⋮ A coherent family of partial functions on ℕ ⋮ Oscillations of sets of integers ⋮ Strongly Baire trees and a cofinal branch principle ⋮ Partition subalgebras for maximal almost disjoint families ⋮ Nonreflecting stationary sets in $\mathcal P_{\kappa}\lambda$ ⋮ Forcing consequences of $PFA$ together with the continuum large ⋮ Generating the club filter on ${\mathcal P}_{\kappa}\lambda$

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