75 papers
This paper investigates the continuous and Borel regulation numbers of rectangular partitions for free -actions on $0n=2n=3n+23\cdot 2^{n-2}$ for higher dimensions, thereby revealing a fundamental distinction in Borel combinatorics between two-dimensional and higher-dimensional cases.
The authors resolve an open question regarding the fragility of Tennenbaum's theorem by constructing a sequence of definitionally equivalent theories for fragments of arithmetic that admit computable nonstandard models, utilizing a new general-purpose strong jump inversion theorem that also unifies several known results.
This paper establishes a machine-checked impossibility result proving that direct compositional measures cannot terminate step-duplicating recursors, while demonstrating that projection-based methods successfully escape this barrier and providing a complete certified termination chain for a minimal witness calculus.
This paper introduces two variations of setwise climbability properties, demonstrating that the first type is equivalent to known principles and consistent with the Proper Forcing Axiom (PFA), while the second type characterizes Martin-type axioms via generalized Banach-Mazur games and is inconsistent with PFA, alongside an analysis of their compatibility with large fragments of PFA.
This paper establishes an analogue of Kaplansky's theorem for models of by introducing -bounded weakly immediate types to prove that every such model possesses a unique --spherical completion, thereby demonstrating that is definably spherically complete.
This paper establishes that the most general "reasonable category of strong vector spaces" admitting formal infinite sums is equivalent to the category of ultrafinite summability spaces, characterizing it as a specific orthogonal subcategory of and analyzing its monoidal closed structures in relation to other categories of topological vector spaces.
This paper introduces a new poset property defined via a variation of the Banach-Mazur game that strengthens -strategic closedness, proves that the Proper Forcing Axiom (PFA) is preserved under forcing with such posets, and applies this result to reproduce Magidor's theorem on the consistency of PFA with weak square principles while distinguishing the property from -operational closedness.
This paper establishes that if a variety of algebras satisfies a strong form of the Eklof-Mekler-Shelah Construction Principle, then almost all of its AEC-coverings of free objects are unsuperstable, with specific applications to -modules and groups.
This paper presents a concise new proof of Van der Waerden's Theorem using algebra in the compact space of ultrafilters , distinguishing itself from existing proofs by avoiding the use of minimal or idempotent ultrafilters.
This paper establishes that in pure polymorphic dependent type theory (P2), parametric quotient types and strong coinduction principles are not definable, and that function extensionality is strictly necessary to prove induction principles, by constructing specific models where these principles fail.
This paper establishes that a weakened version of the Robinson Splitting Theorem, where lowness is replaced by superlowness, holds within models of the theory .
This paper employs model-theoretic methods to establish that generalized strongly normal extensions are Galois extensions of parameterized D-torsors and proves a parameterized version of Kolchin's theorem on differential cohomology to provide a necessary and sufficient condition for such extensions to arise from log-differential equations on their Galois groups.
This paper introduces a geometric rank on imaginaries for the theory of beautiful pairs of algebraically closed fields that refines SU-rank, characterizes forking, and provides an explicit criterion for independence in .
This paper demonstrates that the axioms defining various hypercompositional structures, such as hypergroups and hyperfields, are not independent, and consequently proposes new, minimized definitions that reduce the necessary set of axioms.
This paper introduces the "olive property" as a new sufficient condition for the non-existence of universal groups in certain cardinals, demonstrating that the class of groups satisfies this property despite failing the previously known SOP criterion.