Axiomatizability of second order arithmetic with ω-rule
Non standard interpretations of higher order theories
On the number of models of the Kelley-Morse theory of classes
On partitioner-representability of Boolean algebras
Strongly discrete subsets in ω*
On a theorem of Baumgartner and Weese
On inhomogeneity of products of compact F-spaces
Fat P-sets in the Space ω*
We prove that-consistently-in the space ω* there are no P-sets with the ℂ-cc and any two fat P-sets with the ℂ⁺-cc are coabsolute.
An application of a reflection principle
We define a recursive theory which axiomatizes a class of models of IΔ₀ + Ω ₃ + ¬ exp all of which share two features: firstly, the set of Δ₀ definable elements of the model is majorized by the set of elements definable by Δ₀ formulae of fixed complexity; secondly, Σ₁ truth about the model is recursively reducible to the set of true Σ₁ formulae of fixed complexity.
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