75 papers
This paper analyzes Boolean-valued random forcing in bounded arithmetic from a set-theoretic perspective, demonstrating that under specific saturation assumptions, the forcing algebra is isomorphic to the probability algebra on $2^{\omega_1}$ and establishing the structural relationship between the original model and its generic extensions while offering an alternative framework to axiomatic approaches.
This paper investigates the conditions under which isomorphic copies of the natural numbers preserve the standard class of primitive recursive functions, identifying "bases for punctual standardness" that ensure this invariance while demonstrating that many natural operations fail to satisfy it.
This paper establishes the consistency of the Guessing Model Principle at alongside the existence of an almost Kurepa Suslin tree, demonstrating that the principle can be destructible by a ccc forcing of size , while also proving the consistency of a weak Kurepa tree existing with the failure of the Kurepa Hypothesis and a specific guessing model principle that implies the tree property at .
This paper presents a Coq-based formalization that extends Tarski's mereogeometry into a full topological space by proving the correspondence between mereological classes and regular open sets, thereby reducing Tarski's axiomatic system and enhancing its expressiveness for Euclidean geometric reasoning.
This paper investigates the finite-one structure within the many-one degrees of -rigid sets, demonstrating that such degrees typically contain a least finite-one degree and infinitely many pairwise incomparable finite-one degrees, thereby providing partial solutions to open problems posed by Richter, Stephan, and Zhang.
This paper characterizes split extensions with strong section in the variety of hoops and its key subvarieties using strong external actions, establishing a connection to W. Rump's semidirect product construction in L-algebras and illustrating the theory through the double negation example in BL-algebras.
This paper establishes that the compactness of a finite relational structure is provable within Zermelo-Fraenkel set theory if the structure has width one, but implies the existence of non-measurable sets in three-dimensional space otherwise.
This paper applies Sandqvist's semantics for classical logic without bivalence to metamathematics, demonstrating how this anti-realist framework resolves -incompleteness, establishes induction as meaning-constitutive, and provides an elementary consistency proof for Peano Arithmetic without relying on transfinite ordinals or transcendent truth.
This paper resolves Joel Hamkins' question by proving that no extensional Rosser formula of any complexity exists, while demonstrating that a positive answer holds under the weaker condition of "Conditional Extensionality," which allows for a -formula that is both extensional and -flexible.
This paper establishes the descriptive complexity of various mathematical structures by proving that the Hindman ideal, the ideal , and specific families of trees are -complete, while also exploring the connections between ideals on and classical tree types like Sacks and Miller.
This paper establishes structural results for NIP integral domains, proving that non-field NIP Noetherian domains are semilocal of Krull dimension 1 with characteristic 0 fraction fields, that finite dp-rank domains are henselian local rings, and providing a classification of dp-minimal Noetherian domains.
This paper reviews independence results within Norman Megill's finite axiom-schematization of classical first-order logic and demonstrates that a specific axiom scheme is independent despite all of its individual instances being provable from the remaining schemes.
This paper confirms Martin's conjecture for a broad subclass of weakly quasi-o-minimal theories.
This paper establishes that the Fraïssé limit of the class of Boolean algebras of size less than a strongly inaccessible cardinal (under regular embeddings) shares the same completion as the Lévy collapse, while also providing a direct proof that the collapsing algebra of density cannot be expressed as the union of a -chain of regular sub-algebras of density less than .
This paper defends the significance of Bezboruah and Shepherdson's incompleteness result regarding the weak theory against Kreisel's objections, compares it with Pudlák's extension of the Second Incompleteness Theorem, and provides a new proof based on sequence coding insights from Nielsen and Markov.
This paper proposes a discrete mathematical framework using coarse-grained partitions and categorical unification to quantify information loss in explainable AI, demonstrating that zero loss is an exceptional case and providing a method to optimize the trade-off between interpretability and informational fidelity.
This paper introduces propositional team-based logics that expressively capture dual downward and upward closed properties through variants of inclusion atoms, establishes their normal forms reflecting this duality, and provides sound and complete natural deduction systems for each logic.
This paper introduces the constructive master-modality logics and , proving their EXPTIME-completeness and exponential-size finite model property via translations to , while resolving a conjecture regarding their diamond-free fragment and demonstrating the EXPTIME membership of and through embeddings.
This paper surveys systematic approaches to basis-restricted fragments of propositional and modal logics, leveraging Post's lattice and generalized frameworks to analyze how expressive power and computational complexity depend on allowed operators, while also extending results on learnability and identifying open problems.
This paper demonstrates that the conjugacy relation on one-sided subshifts over the binary alphabet is neither treeable nor amenable from the perspective of descriptive set theory.