7 papers
Every theory is eventually of presheaf type
Christian Espíndola, Kristóf Kanalas
We give a detailed and self-contained introduction to the theory of -toposes and prove the following: 1) A -separable -topos has enough -points. 2) The classifying -…
A short proof of Shelah's eventual categoricity conjecture for AEC's with interpolation, under
Christian Espíndola
We provide a short proof of Shelah's eventual categoricity conjecture, assuming the Generalized Continuum Hypothesis (), for abstract elementary classes (AEC's) with interpola…
Preservation theorems for strong first-order logics
Christian Espíndola
We prove preservation theorems for , the countable fragment of Vaught's closed game logic. These are direct generalizations of the theorems of Łoś-Tarski (res…
A proof of Shelah's eventual categoricity conjecture and an extension to accessible categories with directed colimits
Christian Espíndola
We provide a proof, in , of Shelah's eventual categoricity conjecture for abstract elementary classes (AEC's). Moreover, assuming in addition the Singular Cardinal Hypothesis…
Completeness of infinitary heterogeneous logic
Christian Espíndola
Given a regular cardinal such that (e.g., if the Generalized Continuum Hypothesis holds), we develop a proof system for classical infinitary logic that includes hete…
Constructive completeness and non-discrete languages
Henrik Forssell, Christian Espíndola
We give an analysis and generalizations of some long-established constructive completeness results in terms of categorical logic and pre-sheaf and sheaf semantics. The purpose is i…
Infinitary generalizations of Deligne's completeness theorem
Christian Espíndola
Given a regular cardinal such that , we study a class of toposes with enough points, the -separable toposes. These are equivalent to sheaf toposes over a site with…