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  1. The full basis theorem does not imply analytic wellordering.Vladimir Kanovei & Vassily Lyubetsky - 2021 - Annals of Pure and Applied Logic 172 (4):102929.
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  • Parameterfree Comprehension Does Not Imply Full Comprehension in Second Order Peano Arithmetic.Vladimir Kanovei & Vassily Lyubetsky - forthcoming - Studia Logica:1-16.
    The parameter-free part $$\textbf{PA}_2^*$$ of $$\textbf{PA}_2$$, second order Peano arithmetic, is considered. We make use of a product/iterated Sacks forcing to define an $$\omega $$ -model of $$\textbf{PA}_2^*+ \textbf{CA}(\Sigma ^1_2)$$, in which an example of the full Comprehension schema $$\textbf{CA}$$ fails. Using Cohen’s forcing, we also define an $$\omega $$ -model of $$\textbf{PA}_2^*$$, in which not every set has its complement, and hence the full $$\textbf{CA}$$ fails in a rather elementary way.
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  • A good lightface Δ n 1 well-ordering of the reals does not imply the existence of boldface Δ n − 1 1 well-orderings.Vladimir Kanovei & Vassily Lyubetsky - 2024 - Annals of Pure and Applied Logic 175 (6):103426.
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