arXiv math.LO bot

Replaced article(s) found for math.LO. https://arxiv.org/list/math.LO/new
[1/1]:
- Superabelian logics
Petr Cintula, Filip Jankovec, Carles Noguera
https://arxiv.org/abs/2409.20170

- On Cohesive Products of Fields
Rumen Dimitrov, Valentina Harizanov, Henry J. Klatt, Keshav Srinivasan
https://arxiv.org/abs/2604.09965 @arXiv_mathLO_bot@mastoxiv.page

- An extension of Priestley duality to fuzzy topologies and positive MV-algebras
Marby Zuley Bola\~nos Ortiz, Ciro Russo
https://arxiv.org/abs/2508.19423 @arXiv_mathCT_bot@mastoxiv.page

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Crosslisted article(s) found for math.LO. https://arxiv.org/list/math.LO/new
[1/1]:
- Counting Theorems for Algebraic Relations
Gal Binyamini, Noriko Hirata-Kohno, Makoto Kawashima, Yuval Salant
https://arxiv.org/abs/2604.15189 @arXiv_mathNT_bot@mastoxiv.page

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A rank function for Fra\"{\i}ss\'{e} classes and the rank property

Carlos L\'opez-Callejas, Jareb Navarro-Castillo
https://arxiv.org/abs/2604.14461 https://arxiv.org/pdf/2604.14461 https://arxiv.org/html/2604.14461

arXiv:2604.14461v1 Announce Type: new
Abstract: Given a hereditary class $\mathcal{F}$ of finite relational structures, the rank function $\mathsf{rk}:\sigma\mathcal{F}\to\omega_1\cup\{\infty\}$, introduced by Kubi\'{s} and Shelah, measures how far a countable structure is from being universal within its class: $\mathsf{rk}(X)=\infty$ if and only if the Fra\"{\i}ss\'{e} limit embeds into $X$. We say that $\mathcal{F}$ has the Rank Property (RP) if every countable ordinal is realized as the rank of some $X\in\sigma\mathcal{F}$.
We develop the basic theory of the rank function and establish RP for three families of classes: those satisfying the free amalgamation property and the full extension property (covering graphs, hypergraphs, and many others); finite tournaments; and finite linear orders. For the latter, we compute the rank of every countable ordinal: if $\omega^{\beta_1}\cdot c_1$ is the leading Cantor normal form term of $\alpha\geq\omega$, then $\mathsf{rk}(\alpha)=\omega\cdot\beta_1+\lfloor\log_2 c_1\rfloor$.

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[2026-04-17 Fri (UTC), 1 new article found for math.LO Logic]

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Replaced article(s) found for math.LO. https://arxiv.org/list/math.LO/new
[1/1]:
- On the model theory of the Farey graph
Zahra Mohammadi Khangheshlaghi, Katrin Tent
https://arxiv.org/abs/2503.02121 @arXiv_mathLO_bot@mastoxiv.page

- Modal Exchangeability: Centered Symmetry and the Credal Architecture of Kripke Frames
Daniel Zantedeschi
https://arxiv.org/abs/2603.27547 @arXiv_mathLO_bot@mastoxiv.page

- On Petr Novikov's problem of ordered systems of uniform sets
Vladimir Kanovei, Vassily Lyubetsky
https://arxiv.org/abs/2604.07594 @arXiv_mathLO_bot@mastoxiv.page

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Crosslisted article(s) found for math.LO. https://arxiv.org/list/math.LO/new
[1/1]:
- Topologically valued transition structures
Matthew Collinson
https://arxiv.org/abs/2604.14031 @arXiv_mathCT_bot@mastoxiv.page

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Saturation and isomorphism of abstract harmonic spaces

Haoming Wang
https://arxiv.org/abs/2604.14020 https://arxiv.org/pdf/2604.14020 https://arxiv.org/html/2604.14020

arXiv:2604.14020v1 Announce Type: new
Abstract: This paper models the theory of abstract harmonic spaces in the syntax of the continuous first-order logic of Banach lattices. It addresses a topological question asking when a one-to-one harmonic map onto smooth manifolds $M^n$ is a diffeomorphism. We give $M^n$ ($n\le 2$) a characterization by $U$-rank and elementary saturation for large cardinals. Polar sets are characterized by several equivalent conditions from the omitting type theorem. Consequently, harmonic measures on the ideal boundary in Martin representation are bijectively mapped to Keisler measures supported on non-principal types. Further problems concerning o-minimality and non-local potentials are finally discussed.

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[2026-04-16 Thu (UTC), 1 new article found for math.LO Logic]

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Replaced article(s) found for math.LO. https://arxiv.org/list/math.LO/new
[1/1]:
- Incidence bounds in positive characteristic via valuations and distality
Martin Bays, Jean-Fran\c{c}ois Martin
https://arxiv.org/abs/2104.04339

- A Failure of $\Pi^1_{n+3}$-Reduction in the Presence of $\Sigma^1_{n+3}$-Separation
Stefan Hoffelner
https://arxiv.org/abs/2312.02540 @arXiv_mathLO_bot@mastoxiv.page

- sp-Homogeneous Linear Orderings
Wesley Calvert, Douglas Cenzer, David Gonzalez, Valentina Harizanov, Keng Meng Ng
https://arxiv.org/abs/2509.25005 @arXiv_mathLO_bot@mastoxiv.page

- Perfectoid fields in the language of rings
Franziska Jahnke, Ferr\'eol Lavaud
https://arxiv.org/abs/2602.20847 @arXiv_mathLO_bot@mastoxiv.page

- Dimensional Type Systems and Deterministic Memory Management: Design-Time Semantic Preservation i...
Houston Haynes
https://arxiv.org/abs/2603.16437 @arXiv_csPL_bot@mastoxiv.page

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Crosslisted article(s) found for math.LO. https://arxiv.org/list/math.LO/new
[1/1]:
- Free information geometry and the model theory of noncommutative stochastic processes
David Jekel
https://arxiv.org/abs/2604.12212 @arXiv_mathOA_bot@mastoxiv.page

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From Witness-Space Sharpness To Family-Pointwise Exactness For The Solvability Complexity Index

Christopher Sorg
https://arxiv.org/abs/2604.12750 https://arxiv.org/pdf/2604.12750 https://arxiv.org/html/2604.12750

arXiv:2604.12750v1 Announce Type: new
Abstract: We study how exact Solvability Complexity Index (SCI) statements should be formulated for families of computational problems rather than for single problems. While the equality \(\operatorname{SCI}_G (\mathcal P)=k\) is unambiguous for an individual computational problem \(\mathcal P\), the family setting requires one to distinguish family-pointwise exactness, witness-space sharpness, and worst-case exactness. We formalize this trichotomy, prove that witness-space sharpness coincides with worst-case exactness but is, in general, strictly weaker than family-pointwise exactness, and show that certain Koopman-operator classification results are sharp only in this worst-case sense.
We then establish two positive upgrade theorems: an abstract pullback principle and a concrete finite-query criterion guaranteeing that witness-space sharpness upgrades to family-pointwise exactness. Next, we introduce a decoder-regular finite-query transport preorder on SCI computational problems, prove that it is a preorder, derive a transport-saturation sufficient criterion extending the principal-source package, and show that the associated transport degrees need not form a lattice in full generality. We analyze the natural decoder classes \(\mathscr R_{\mathrm{cont}}\) and \(\mathscr R_{\mathrm{Bor}}\): on the full class the corresponding quotients are not upper semilattices, while on the nondegenerate subclass the preorder is upward and downward directed. Finally, we exhibit two natural positive families realizing the principal transport mechanism: exact integration on compact intervals and a fixed-window spectral decision family obtained by block-diagonal stabilization.

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On a new theory of models for formal mathematical systems

Matthias Kunik
https://arxiv.org/abs/2604.12432 https://arxiv.org/pdf/2604.12432 https://arxiv.org/html/2604.12432

arXiv:2604.12432v1 Announce Type: new
Abstract: We study a new model theory for formal mathematical systems that we developed in a previous paper. We introduce isomorphic and homomorphic structures for formal languages, present some results and examples and conclude our paper with a discussion about the reduced set theory RST adapted to our new theory.

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Transitive Extensions of Automorphism Groups of Generic Structures

Felipe Estrada
https://arxiv.org/abs/2604.12146 https://arxiv.org/pdf/2604.12146 https://arxiv.org/html/2604.12146

arXiv:2604.12146v1 Announce Type: new
Abstract: This work addresses the existence of transitive extensions of certain infinite permutation groups which arise as the automorphism groups of model-theoretic structures which are generic in the Fra\"iss\'e sense. The study of transitive extensions has hitherto largely concerned itself with finite permutation groups. Moving beyond the finite realm, we develop combinatorial tools to prove that transitive extensions exist for edge-colored k-hypergraphs only when the number of colors is a power of two and that transitive extensions exist for k-hypertournaments (in the Cherlin sense) only when k is even, among other results.

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[2026-04-15 Wed (UTC), 3 new articles found for math.LO Logic]

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Crosslisted article(s) found for math.LO. https://arxiv.org/list/math.LO/new
[1/1]:
- Normed lattices majorizing in their norm completions
Eugene Bilokopytov, Viktor Bohdanskyi
https://arxiv.org/abs/2604.09939 @arXiv_mathFA_bot@mastoxiv.page

- A Linear Temporal Logic of Frequencies on Series of Events
Melissa Antonelli, Leonardo Ceragioli, Alessandro Buda, Giuseppe Primiero
https://arxiv.org/abs/2604.10669 @arXiv_csLO_bot@mastoxiv.page

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A computably enumerable many-one degree with no least finite-one degree

Patrizio Cintioli
https://arxiv.org/abs/2604.10879 https://arxiv.org/pdf/2604.10879 https://arxiv.org/html/2604.10879

arXiv:2604.10879v1 Announce Type: new
Abstract: Richter, Stephan, and Zhang asked whether every nonrecursive many-one degree contains a least finite-one degree. We solve this question in the negative, already within the class of computably enumerable many-one degrees. Positive answers are known in two disjoint natural settings: for a measure-one and comeager class of $m$-rigid sets, and, in a companion paper, for computably enumerable many-one degrees containing a $D$-maximal set. We construct a nonrecursive \ce\ set $A$ such that for every set $X \eqm A$ there exists a c.e.\ set $B \eqm A$ with $X \not\lfo B$. Hence the many-one degree of $A$ contains no least finite-one degree. The proof is a finite-injury priority construction based on virtual target sets and a dynamic trap mechanism forcing any putative finite-one reduction either to violate finite-oneness or to compute an incorrect reduction.

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Iterating Generalised Perfect Set Forcing Along Well-Founded Orders

Mirna D\v{z}amonja
https://arxiv.org/abs/2604.10826 https://arxiv.org/pdf/2604.10826 https://arxiv.org/html/2604.10826

arXiv:2604.10826v1 Announce Type: new
Abstract: Vladimir Kanovei \cite{zbMATH01335192} developed the technique of geometric iteration and used it to prove that the perfect set forcing can be iterated with countable supports along any partial order, while preserving $\aleph_1$. In \cite{Property-B} we considered a generalised perfect set forcing with respect to a filter on a cardinal $\kappa$ satisfying $\kappa^{<\kappa}=\kappa$, which we denoted ${\mathbb P} (\mathcal F)$, and proved that its iteration with supports of size $\le\kappa$ along any ordinal preserves cardinals up and including $\kappa^+$.
We show that there is a version of the geometric iteration technique that applies to ${\mathbb P} (\mathcal F)$, to yield that for $\kappa$ satisfying $\kappa^{<\kappa}=\kappa$, the forcing ${\mathbb P} (\FF)$ can be iterated with supports of size $\le\kappa$ along any well-founded partial order, while preserving cardinals up and including $\kappa^+$.

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A note on iterating strongly $(<\lambda)$-closed stationary $\lambda^+$-cc forcing

Mirna D\v{z}amonja
https://arxiv.org/abs/2604.10713 https://arxiv.org/pdf/2604.10713 https://arxiv.org/html/2604.10713

arXiv:2604.10713v1 Announce Type: new
Abstract: We give an exposition of an iteration theorem for iterating $(<\lambda)$-closed stationary $\lambda^+$-cc forcing with supports of size $<\lambda$ and preserving these two properties. We discuss the relation of this theorem with other iteration theorems and forcing axioms that have appeared in the literature, notably the one from \cite{Sh80}.

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Almost Free Non-Archimedean Banach Spaces and Relation to Large Cardinals

Tomoki Mihara
https://arxiv.org/abs/2604.10526 https://arxiv.org/pdf/2604.10526 https://arxiv.org/html/2604.10526

arXiv:2604.10526v1 Announce Type: new
Abstract: Let $k$ be a complete valuation field. We formulate a free Banach $k$-vector space as a Banach $k$-vector space with an orthonormal Schauder basis, and an almost free Banach $k$-vector space as a non-Archimedean analogue of an almost free Abelian group. As non-Archimedean analogues of the classical facts that an almost free Abelian group is free under the assumption of the $\aleph_1$-strong compactness or the weak compactness of the cardinality, we show that an almost free Banach $k$-vector space is free under similar assumptions.

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The automorphism group of countable recursively saturated models of Peano arithmetic and strong cuts

Saeideh Bahrami
https://arxiv.org/abs/2604.10282 https://arxiv.org/pdf/2604.10282 https://arxiv.org/html/2604.10282

arXiv:2604.10282v1 Announce Type: new
Abstract: In this paper, we extend the concept of a Lascar generic automorphism in the setting of models of Peano arithmetic ($\mathrm{PA}$) to the subgroup of the automorphism group of a countable recursively saturated model $\mathcal{M}$ of $\mathrm{PA}$ that fixes pointwise a strong cut $I$ of $\mathcal{M}$, denoted by $(\mathrm{Aut}(\mathcal{M}))_{(I)}$. Then, we prove that:
(1) $(\mathrm{Aut}(\mathcal{M}))_{(I)}$ has the small index property.
(2) The cofinality of $(\mathrm{Aut}(\mathcal{M}))_{(I)}$ is uncountable.
(3) Any nontrivial normal subgroup of $(\mathrm{Aut}(\mathcal{M}))_{(I)}$ is meagre in it. In particular, the infinite cyclic group $\mathbb{Z}$ is not a homomorphic image of $(\mathrm{Aut}(\mathcal{M}))_{(I)}$.

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