Displaying similar documents to “Addendum to “A note on the MacDowell–Specker theorem””

On extending automorphisms of models of Peano Arithmetic

Roman Kossak, Henryk Kotlarski (1996)

Fundamenta Mathematicae

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Continuing the earlier research in [10] we give some information on extending automorphisms of models of PA to end extensions and cofinal extensions.

The distributivity numbers of finite products of P(ω)/fin

Saharon Shelah, Otmar Spinas (1998)

Fundamenta Mathematicae

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Generalizing [ShSp], for every n < ω we construct a ZFC-model where ℌ(n), the distributivity number of r.o. ( P ( ω ) / f i n ) n , is greater than ℌ(n+1). This answers an old problem of Balcar, Pelant and Simon (see [BaPeSi]). We also show that both Laver and Miller forcings collapse the continuum to ℌ(n) for every n < ω, hence by the first result, consistently they collapse it below ℌ(n).

Universal spaces in the theory of transfinite dimension, I

Wojciech Olszewski (1994)

Fundamenta Mathematicae

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R. Pol has shown that for every countable ordinal α, there exists a universal space for separable metrizable spaces X with ind X = α . We prove that for every countable limit ordinal λ, there is no universal space for separable metrizable spaces X with Ind X = λ. This implies that there is no universal space for compact metrizable spaces X with Ind X = λ. We also prove that there is no universal space for compact metrizable spaces X with ind X = λ.

Chains and antichains in Boolean algebras

M. Losada, Stevo Todorčević (2000)

Fundamenta Mathematicae

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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.