Lindenbaum algebras and model companions
Linear and -linear betweenness spaces
Linear extenders and the Axiom of Choice
In set theory without the Axiom of Choice ZF, we prove that for every commutative field , the following statement : “On every non null -vector space, there exists a non null linear form” implies the existence of a “-linear extender” on every vector subspace of a -vector space. This solves a question raised in Morillon M., Linear forms and axioms of choice, Comment. Math. Univ. Carolin. 50 (2009), no. 3, 421-431. In the second part of the paper, we generalize our results in the case of spherically...
Linear forms and axioms of choice
We work in set-theory without choice ZF. Given a commutative field , we consider the statement : “On every non null -vector space there exists a non-null linear form.” We investigate various statements which are equivalent to in ZF. Denoting by the two-element field, we deduce that implies the axiom of choice for pairs. We also deduce that implies the axiom of choice for linearly ordered sets isomorphic with .
Linear identities in graph algebras
We find the basis of all linear identities which are true in the variety of entropic graph algebras. We apply it to describe the lattice of all subvarieties of power entropic graph algebras.
Linear orders and MA + ¬wKH
I prove that the statement that “every linear order of size can be embedded in ” is consistent with MA + ¬ wKH.
Linear topologies on sesquilinear spaces of uncountable dimension
Lipschitz-quotients and the Kunen-Martin Theorem
We show that there is a universal control on the Szlenk index of a Lipschitz-quotient of a Banach space with countable Szlenk index. It is in particular the case when two Banach spaces are Lipschitz-homeomorphic. This provides information on the Cantor index of scattered compact sets and such that is a Lipschitz-quotient of (that is the case in particular when these two spaces are Lipschitz-homeomorphic). The proof requires tools of descriptive set theory.
L-like Combinatorial Principles and Level by Level Equivalence
We force and construct a model in which GCH and level by level equivalence between strong compactness and supercompactness hold, along with certain additional “L-like” combinatorial principles. In particular, this model satisfies the following properties: (1) holds for every successor and Mahlo cardinal δ. (2) There is a stationary subset S of the least supercompact cardinal κ₀ such that for every δ ∈ S, holds and δ carries a gap 1 morass. (3) A weak version of holds for every infinite cardinal...
Löb operators and interior operators
Local analysis for semi-bounded groups
An o-minimal expansion ℳ = ⟨M,<,+,0, ...⟩ of an ordered group is called semi-bounded if it does not expand a real closed field. Possibly, it defines a real closed field with bounded domain I ⊆ M. Let us call a definable set short if it is in definable bijection with a definable subset of some Iⁿ, and long otherwise. Previous work by Edmundo and Peterzil provided structure theorems for definable sets with respect to the dichotomy ’bounded versus unbounded’. Peterzil (2009) conjectured a refined...
Local analysis of nonstandard functions of pre-distributional type
Local normal forms for first-order logic with applications to games and automata.
Local properties of complete Boolean products
Local-global convergence, an analytic and structural approach
Based on methods of structural convergence we provide a unifying view of local-global convergence, fitting to model theory and analysis. The general approach outlined here provides a possibility to extend the theory of local-global convergence to graphs with unbounded degrees. As an application, we extend previous results on continuous clustering of local convergent sequences and prove the existence of modeling quasi-limits for local-global convergent sequences of nowhere dense graphs.
Localic completion of generalized metric spaces I.
Localization o a theorem of Ambos-Spies and the strong anti-splitting property.
Locally compact linearly Lindelöf spaces
There is a locally compact Hausdorff space which is linearly Lindelöf and not Lindelöf. This answers a question of Arhangel'skii and Buzyakova.
Locally compact perfectly normal spaces may all be paracompact
We work towards establishing that if it is consistent that there is a supercompact cardinal then it is consistent that every locally compact perfectly normal space is paracompact. At a crucial step we use some still unpublished results announced by Todorcevic. Modulo this and the large cardinal, this answers a question of S. Watson. Modulo these same unpublished results, we also show that if it is consistent that there is a supercompact cardinal, it is consistent that every locally compact space...
Locally constant functions
Let X be a compact Hausdorff space and M a metric space. is the set of f ∈ C(X,M) such that there is a dense set of points x ∈ X with f constant on some neighborhood of x. We describe some general classes of X for which is all of C(X,M). These include βℕ, any nowhere separable LOTS, and any X such that forcing with the open subsets of X does not add reals. In the case where M is a Banach space, we discuss the properties of as a normed linear space. We also build three first countable Eberlein...