92 research outputs found
Model theory of operator algebras III: Elementary equivalence and II_1 factors
We use continuous model theory to obtain several results concerning
isomorphisms and embeddings between II_1 factors and their ultrapowers. Among
other things, we show that for any II_1 factor M, there are continuum many
nonisomorphic separable II_1 factors that have an ultrapower isomorphic to an
ultrapower of M. We also give a poor man's resolution of the Connes Embedding
Problem: there exists a separable II_1 factor such that all II_1 factors embed
into one of its ultrapowers.Comment: 16 page
Algebraic combinatorics in bounded induction
In this paper, new methods for analyzing models of weak subsystems of Peano Arithmetic are proposed. The focus will be on the study of algebro-combinatoric properties of certain definable cuts. Their relationship with segments that satisfy more induction, with those limited by the standard powers/roots of an element, and also with definable sets in Bounded Induction is studied. As a consequence, some considerations on the Π1-interpretability of IΔ0 in weak theories, as well as some alternative axiomatizations, are reviewed. Some of the results of the paper are obtained by immersing Bounded Induction models in its Stone-Cech Compactification, once it is endowed with a topology.Ministerio de Ciencia, Innovación y Universidades PID2019-109152GB-I0
On Deciding Local Theory Extensions via E-matching
Satisfiability Modulo Theories (SMT) solvers incorporate decision procedures
for theories of data types that commonly occur in software. This makes them
important tools for automating verification problems. A limitation frequently
encountered is that verification problems are often not fully expressible in
the theories supported natively by the solvers. Many solvers allow the
specification of application-specific theories as quantified axioms, but their
handling is incomplete outside of narrow special cases.
In this work, we show how SMT solvers can be used to obtain complete decision
procedures for local theory extensions, an important class of theories that are
decidable using finite instantiation of axioms. We present an algorithm that
uses E-matching to generate instances incrementally during the search,
significantly reducing the number of generated instances compared to eager
instantiation strategies. We have used two SMT solvers to implement this
algorithm and conducted an extensive experimental evaluation on benchmarks
derived from verification conditions for heap-manipulating programs. We believe
that our results are of interest to both the users of SMT solvers as well as
their developers
The Modal Logics of Kripke-Feferman Truth
We determine the modal logic of fixed-point models of truth and their axiomatizations by Solomon Feferman via Solovay-style completeness results
The Modal Logics of Kripke-Feferman Truth
We determine the modal logic of fixed-point models of truth and their
axiomatizations by Solomon Feferman via Solovay-style completeness results.
Given a fixed-point model , or an axiomatization thereof, we
find a modal logic such that a modal sentence is a theorem of
if and only if the sentence obtained by translating the modal
operator with the truth predicate is true in or a theorem of
under all such translations. To this end, we introduce a novel version of
possible worlds semantics featuring both classical and nonclassical worlds and
establish the completeness of a family of non-congruent modal logics whose
internal logic is subclassical with respect to this semantics
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