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CH and the Sacks property

S. Quickert (2002)

Fundamenta Mathematicae

We show the consistency of CH and the statement “no ccc forcing has the Sacks property” and derive some consequences for ccc ω ω -bounding forcing notions.

Chain conditions in maximal models

Paul Larson, Stevo Todorčević (2001)

Fundamenta Mathematicae

We present two m a x varations which create maximal models relative to certain counterexamples to Martin’s Axiom, in hope of separating certain classical statements which fall between MA and Suslin’s Hypothesis. One of these models is taken from [19], in which we maximize relative to the existence of a certain type of Suslin tree, and then force with that tree. In the resulting model, all Aronszajn trees are special and Knaster’s forcing axiom ₃ fails. Of particular interest is the still open question...

Chains and antichains in Boolean algebras

M. Losada, Stevo Todorčević (2000)

Fundamenta Mathematicae

We give an affirmative answer to problem DJ from Fremlin’s list [8] which asks whether M A ω 1 implies that every uncountable Boolean algebra has an uncountable set of pairwise incomparable elements.

Characteristic of Rings. Prime Fields

Christoph Schwarzweller, Artur Korniłowicz (2015)

Formalized Mathematics

The notion of the characteristic of rings and its basic properties are formalized [14], [39], [20]. Classification of prime fields in terms of isomorphisms with appropriate fields (ℚ or ℤ/p) are presented. To facilitate reasonings within the field of rational numbers, values of numerators and denominators of basic operations over rationals are computed.

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