3 citations · 4 across the 5 of their papers we have counts for
5 papers
New bounds on the strength of some restrictions of Hindman's Theorem
Lorenzo Carlucci, Leszek Aleksander Kołodziejczyk, Francesco Lepore +1
We prove upper and lower bounds on the effective content and logical strength for a variety of natural restrictions of Hindman's Finite Sums Theorem. For example, we show that Hind…
Second order intuitionistic propositional logic of the real line is decidable
Konrad Zdanowski
It is known that the set of tautologies of second order intuitionistic propositional logic, , is undecidable. Here, we prove that the sets of formulas of $\mathrm{I…
One Henkin Quantifier in the empty vocabulary suffices for undecidability
Konrad Zdanowski
We prove that there are single Henkin quantifiers such that first order logic augmented by one of these quantifiers is undecidable in the empty vocabulary. Examples of such quantif…
On the Mints Hierarchy in First-Order Intuitionistic Logic
Aleksy Schubert, Paweł Urzyczyn, Konrad Zdanowski
We stratify intuitionistic first-order logic over into fragments determined by the alternation of positive and negative occurrences of quantifiers (Mints hierarchy)…
The strength of Ramsey Theorem for coloring relatively large sets
Lorenzo Carlucci, Konrad Zdanowski
We characterize the computational content and the proof-theoretic strength of a Ramsey-type theorem for bi-colorings of so-called {\em exactly large} sets. An {\it exactly large} s…