Logic Papers
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Logic, set theory, point-set topology, formal mathematics - new submissions to https://t.co/gg4TMq7eu9 (not affiliated with arXiv)
Joined November 2010
An abstract fixed-point theorem for Horn formula equations.
arxiv.org
We consider a class of formula equations in first-order logic, Horn formula equations, which are defined by a syntactic restriction on the occurrences of predicate variables. Horn formula...
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Omega-categorical groups and rings of finite dimension.
arxiv.org
We prove that a finite-dimensional omega-categorical group is finite-by-abelian-by-finite and that a finite-dimensional omega-categorical ring is virtually finite-by-null.
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First-Order Axiom Systems $\mathscr{E}_{d}$ and $\mathscr{E}_{da}$ Extending Tarski's $\mathscr{E}_{2}$ with Distance and Angle Function Symbols for Quantitative Euclidean Geometry.
arxiv.org
Tarski's first-order axiom system $\mathscr{E}_{2}$ for Euclidean geometry is notable for its completeness and decidability. However, the Pythagorean theorem -- either in its modern algebraic form...
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Symmetric Iterations with Countable and $<\kappa$-Support: A Framework for Choiceless ZF Extensions.
arxiv.org
We present a unified framework for symmetric iterations with countable and, more generally, $<κ$ support. Set-length iterations are handled uniformly, and when driven by a first-order...
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On the Realizability of Prime Conjectures in Heyting Arithmetic.
arxiv.org
We show that no total functional can uniformly transform $Π_1$ primality into explicit $Σ_1$ witnesses without violating normalization in $\mathsf{HA}$. The argument proceeds through three...
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Partition Principle without Choice via Symmetric Iterations and Sheaf-Toposes.
arxiv.org
The Partition Principal ($\mathsf{PP}$) asserts that every surjection $A\twoheadrightarrow B$ admits an injection $B\hookrightarrow A$. In $\mathsf{ZF}$, $\mathsf{AC}$ implies $\mathsf{PP}$, and...
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On the strength of ultrafilters above choiceless large cardinals and their Prikry forcings.
arxiv.org
We study the strength of well-founded ultrafilters on ordinals above choiceless large cardinals and their associated Prikry forcings. Gabriel Goldberg showed that all but boundedly many regular...
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On the Various Translations between Classical, Intuitionistic and Linear Logic.
arxiv.org
Several different proof translations exist between classical and intuitionistic logic (negative translations), and intuitionistic and linear logic (Girard translations). Our aims in this paper are...
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Measuring the complexity of characterizing $[0, 1]$, $S^1$, and $\mathbb{R}$ up to homeomorphism.
arxiv.org
In analogy to the study of Scott rank/complexity of countable structures, we initiate the study of the Wadge degrees of the set of homeomorphic copies of topological spaces. One can view our...
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An Algebraic Abstraction of the Localic Sheafification via the Tripos-to-Topos Construction.
arxiv.org
Localic and realizability toposes are two central classes of toposes in categorical logic, both arising through the Hyland-Johnstone-Pitts tripos-to-topos construction. We investigate their shared...
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Eventual Capture on a Measurable Cardinal.
arxiv.org
We continue the study from \cite{BrendleFreidmanMontoya, vandervlugtlocalizationcardinals} of localization cardinals $\mfb_κ(\in^*)$ and $\mfd_κ(\in^*)$ and their variants at regular...
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Abstract independence relations in neostability theory.
arxiv.org
We develop a framework, in the style of Adler, for interpreting the notion of "witnessing" that has appeared (usually as a variant of Kim's Lemma) in different areas of neostability theory as a...
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A new representation of finite Hoops using a new type of product of structures.
arxiv.org
In this paper we show that a new type of products hoops can be defined which, in the case of finite hoops, can describe an arbitrary hoop $\mathbf A$ as the product of its arbitrary filter $F$ and...
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The epimorphism relation among countable groups is a complete analytic quasi-order.
arxiv.org
We prove that the epimorphism relation is a complete analytic quasi-order on the space of countable groups. In the process we obtain the result of indepent interest showing that the epimorphism...
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Structures of uninorms on bounded lattices via t-conorms, closure operators and t-subnorms.
arxiv.org
In this paper, we provide some structures of uninorms on bounded lattices via t-conorms, closure operators and t-subnorms, subject to certain constraints on the closure operators and t-subnorms....
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Notions of rank and independence in countably categorical theories.
arxiv.org
For an $ω$-categorical theory $T$ and model $\mathcal{M}$ of $T$ we define a hierarchy of ranks, the $n$-ranks for $n < ω$ which only care about imaginary elements ``up to level $n$'',...
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