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Bibliographic Details
Main Author:	Troiani, William
Format:	Preprint
Published:	2025
Subjects:	Logic 18C20
Online Access:	https://arxiv.org/abs/2504.10805
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Finite approximation of free groups II: the Theorems of Ash, Herwig-Lascar and Ribes-Zalesskii -- revisited and strengthened
by: Auinger, K., et al.
Published: (2025)

On Ramsey degrees, compactness and approximability
by: Mašulović, Dragan
Published: (2024)

An Internal Logic of Virtual Double Categories
by: Nasu, Hayato
Published: (2024)

On the Category-Theoretic Independence of Meaning, Object, Name and Existence
by: Inoué, Takao
Published: (2026)

Colimits of Heyting Algebras through Esakia Duality
by: Almeida, Rodrigo Nicolau
Published: (2024)

Implicit operations in varieties of commutative monoids
by: Carai, Luca, et al.
Published: (2026)

Finite axiomatizability of the rank and the dimension of a pro-$π$ group
by: Conte, Martina, et al.
Published: (2023)

Profinite rigidity of crystallographic groups arising from Lie theory
by: Carolillo, Davide, et al.
Published: (2025)

Cofibrant generation of pure monomorphisms in presheaf categories
by: Cox, Sean, et al.
Published: (2025)

Linear Logic and the Hilbert Scheme
by: Troiani, William, et al.
Published: (2025)

An unusual example of a universal automorphism group
by: Sullivan, Rob, et al.
Published: (2026)

Free Doubly-Infinitary Distributive Categories are Cartesian Closed
by: Nunes, Fernando Lucatelli, et al.
Published: (2024)

Linear Logic and Quantum Error Correcting Codes
by: Murfet, Daniel, et al.
Published: (2024)

A Topos-Theoretic Semantics of Intuitionistic Modal Logic with an Application to the Logic of Branching Spacetime
by: Lambert, Michael J.
Published: (2024)

Extensive embeddings into Fraïssé structures and stationary weak independence relations
by: Kwiatkowska, Aleksandra, et al.
Published: (2025)

Wilson conjecture for omega-categorical Lie algebras, the case 4-Engel characteristic 3
by: d'Elbée, Christian
Published: (2024)

Sharply k-transitive actions on ultrahomogeneous structures
by: González, J. de la Nuez, et al.
Published: (2025)

Logic and Concepts in the 2-category of Topoi
by: Di Liberti, Ivan, et al.
Published: (2025)

A characterization of Continuous Logic by using quantale-valued logics
by: Reyes, David, et al.
Published: (2021)

Bundles of metric structures as left ultrafunctors
by: Hamad, Ali
Published: (2024)

A Note on Los's Theorem for Kripke-Joyal Semantics
by: Aiguier, Marc, et al.
Published: (2024)

Epimorphisms between finitely generated algebras
by: Carai, Luca, et al.
Published: (2024)

Universal homogeneous two-sorted ultrametric spaces
by: Bartoš, Adam, et al.
Published: (2026)

Conciseness of first-order formulae
by: Conte, Martina, et al.
Published: (2025)

TAPO-Description Logic for Information Behavior: Refined OBoxes, Inference, and Categorical Semantics
by: Inoué, Takao
Published: (2026)

Existential completions and Herbrand's theorem
by: Wrigley, Joshua L.
Published: (2025)

Wilson conjecture for omega-categorical Lie algebras, the case 3-Engel characteristic 5
by: d'Elbée, Christian
Published: (2024)

Generalised ultracategories and conceptual completeness of geometric logic
by: Hamad, Ali
Published: (2025)

On the lack of colimits in various categories arising in pointfree topology and algebraic logic
by: Abbadini, Marco, et al.
Published: (2025)

From coextensive varieties to the Gaeta topos
by: Zuluaga, William
Published: (2022)

Coslice Colimits in Homotopy Type Theory
by: Hart, Perry, et al.
Published: (2024)

TAPO-Structured Description Logic for Information Behavior: Procedural and Oracle-Based Extensions
by: Inoué, Takao
Published: (2026)

Profunctorial algebras
by: Aristote, Quentin, et al.
Published: (2026)

A completion of reduced commutative rings
by: Carai, Luca, et al.
Published: (2026)

Higher inductive types in $(\infty,1)$-categories
by: Uemura, Taichi
Published: (2024)

Generic groups and the weak amalgamation property
by: Ivanov, Aleksander, et al.
Published: (2024)

Dialectica Petri Nets
by: Di Lavore, Elena, et al.
Published: (2021)

Categorical Framework for Typed Extensional and Intensional Models in Formal Semantics
by: Quigley, Daniel
Published: (2024)

2-classifiers via dense generators and Hofmann-Streicher universe in stacks
by: Mesiti, Luca
Published: (2024)

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// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

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