Medvedev logic is undecidable

The paper reduces periodic plane tiling to non-theoremhood in Medvedev logic and proves $\mathsf{ML}$ is undecidable and not recursively axiomatizable. A modification also proves undecidability of Skvortsov logic for infinite problems, and shows the two logics can be separated using any aperiodic plane tiling. Both papers are preprints, so the result should remain a review-pending candidate.

The paper reduces periodic plane tiling to non-theoremhood in Medvedev logic and proves $\mathsf{ML}$ is undecidable and not recursively axiomatizable. A modification also proves undecidability of Skvortsov logic for infinite problems, and shows the two logics can be separated using any aperiodic plane tiling. Both papers are preprints, so the result should remain a review-pending candidate.