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

P. Clote

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On extending automorphisms of models of Peano Arithmetic

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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.

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Strong arithmetic properties of the integral solutions of X³ + DY³ + D²Z³ - 3DXYZ = 1, where D = M³ ± 1, M ∈ ℤ*

Christian Ballot (1999)

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A cardinal preserving immune partition of the ordinals

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

Saharon Shelah, Otmar Spinas (1998)

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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).

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Universal spaces in the theory of transfinite dimension, I

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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

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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.