21 citations · 76 across the 13 of their papers we have counts for
19 papers
Induced and higher-dimensional stable independence
Michael Lieberman, Jiri Rosicky, Sebastien Vasey
We provide several crucial technical extensions of the theory of stable independence notions in accessible categories. In particular, we describe circumstances under which a stable…
Cofibrant generation of pure monomorphisms
Michael Lieberman, Leonid Positselski, Jiri Rosicky +1
We show that pure monomorphisms are cofibrantly generated---generated from a set of morphisms by pushouts, transfinite composition, and retracts---in any locally finitely presentab…
Hilbert spaces and -algebras are not finitely concrete
Michael Lieberman, Jiří Rosický, Sebastien Vasey
We show that no faithful functor from the category of Hilbert spaces with linear isometries into the category of sets preserves directed colimits. Thus Hilbert spaces cannot form a…
Cellular categories and stable independence
Michael Lieberman, Jiří Rosický, Sebastien Vasey
We exhibit a bridge between the theory of cellular categories, used in algebraic topology and homological algebra, and the model-theoretic notion of stable independence. Roughly sp…
Tameness, powerful images, and large cardinals
Will Boney, Michael Lieberman
We provide comprehensive, level-by-level characterizations of large cardinals, in the range from weakly compact to strongly compact, by closure properties of powerful images of acc…
Sizes and filtrations in accessible categories
Michael Lieberman, Jiří Rosický, Sebastien Vasey
Accessible categories admit a purely category-theoretic replacement for cardinality: the internal size. Generalizing results and methods from arXiv:1708.06782, we examine set-theor…
Tameness in generalized metric structures
Michael Lieberman, Jiri Rosicky, Pedro Zambrano
We broaden the framework of metric abstract elementary classes (mAECs) in several essential ways, chiefly by allowing the metric to take values in a well-behaved quantale. As a pro…
A category-theoretic characterization of almost measurable cardinals
Michael Lieberman
Through careful analysis of an argument of Brooke-Taylor and Rosicky, we show that the powerful image of any accessible functor is closed under colimits of -chains, a suffic…
Forking independence from the categorical point of view
Michael Lieberman, Jiří Rosický, Sebastien Vasey
Forking is a central notion of model theory, generalizing linear independence in vector spaces and algebraic independence in fields. We develop the theory of forking in abstract, c…
Internal sizes in -abstract elementary classes
Michael Lieberman, Jiří Rosický, Sebastien Vasey
Working in the context of -abstract elementary classes (-AECs) - or, equivalently, accessible categories with all morphisms monomorphisms - we examine the two natural notions…
Universal abstract elementary classes and locally multipresentable categories
Michael Lieberman, Jiří Rosický, Sebastien Vasey
We exhibit an equivalence between the model-theoretic framework of universal classes and the category-theoretic framework of locally multipresentable categories. We similarly give…
Hanf numbers via accessible images
Michael Lieberman, Jiri Rosicky
We present several new model-theoretic applications of the fact that, under the assumption that there exists a proper class of almost strongly compact cardinals, the powerful image…
-Abstract Elementary Classes and other generalizations
Will Boney, Rami Grossberg, Michael Lieberman +2
We introduce -Abstract Elementary Classes (-AECs) as a broad framework for model theory that includes complete boolean algebras and Dirichlet series, and begin to develop the…
Approximations of superstability in concrete accessible categories
Michael Lieberman, Jiri Rosicky
We generalize the constructions and results of Chapter 10 in Baldwin's "Categoricity" to coherent accessible categories with concrete directed colimits and concrete monomorphisms.…
Limits of abstract elementary classes
M. Lieberman, J. Rosický
We show that the category of abstract elementary classes (AECs) and concrete functors is closed under constructions of "limit type," which generalizes the approach of Mariano, Zamb…
Metric abstract elementary classes as accessible categories
Michael Lieberman, Jiri Rosicky
We show that metric abstract elementary classes (mAECs) are, in the sense of [LR] (i.e. arXiv:1404.2528), coherent accessible categories with directed colimits, with concrete $\ale…
Classification theory for accessible categories
Michael Lieberman, Jirí Rosický
We show that a number of results on abstract elementary classes (AECs) hold in accessible categories with concrete directed colimits. In particular, we prove a generalization of a…
Rank functions and partial stability spectra for tame AECs
Michael Lieberman
We introduce a family of rank functions and related notions of total transcendence for Galois types in abstract elementary classes. We focus, in particular, on abstract elementary…
A Topology for Galois Types in AECs
Michael Lieberman
We present a way of topologizing sets of Galois types over structures in abstract elementary classes with amalgamation. In the elementary case, the topologies thus produced refine…