1 - 10 of 11 articles
We sharpen Hájek’s Completeness Theorem for theories extending predicate product logic,
. By relating provability in this system to embedding properties of ordered abelian groups we construct a universal BL-chain L in the sense that a sentence is provable from...
We introduce new proof systems G[β] and G
ext[β], which are equivalent to the standard equational calculi of λβ- and λβη- conversion, and which may be qualified as ‘analytic’ because it is possible to establish, by purely proof-theoretical methods, that in both of them the transitivity rule...
Using sheaves of special groups, we show that a general local-global principle holds for every reduced special group whose associated space of orderings only has a finite number of accumulation points. We also compute the behaviour of the Boolean hull functor applied to sheaves of special groups.
We prove that a countable, complete, first-order theory with infinite dcl(
$$ \theta $$
) and precisely three non-isomorphic countable models interprets a variant of Ehrenfeucht’s or Peretyatkin’s example.
In their paper from 1981, Milner and Sauer conjectured that for any poset
, then P must contain an antichain of size κ. We prove that for λ > cf(λ) = κ, if there exists a cardinal μ < λ such that cov(λ, μ, κ, 2) = λ, then...
We define a theory of two-sort bounded arithmetic whose provably total functions are exactly those in
by way of a generalized quantifier that expresses computations of SAC
1 circuits. The proof depends on Kolokolova’s conditions for the connection between the provable...
In this paper, we show within
that both the Jordan curve theorem and the Schönflies theorem are equivalent to weak König’s lemma. Within
, we prove the Jordan curve theorem using an argument of non-standard analysis based on the fact that every...
Axiomatizations are presented for fuzzy logics characterized by uninorms continuous on the half-open real unit interval [0,1), generalizing the continuous t-norm based approach of Hájek. Basic uninorm logic BUL is defined and completeness is established with respect to algebras with lattice...
A method is described for obtaining conjunctive normal forms for logics using Gentzen-style rules possessing a special kind of strong invertibility. This method is then applied to a number of prominent fuzzy logics using hypersequent rules adapted from calculi defined in the literature. In...
Hirschfeld and Wheeler proved in 1975 that ∑1 ultrapowers (= “simple models”) are rigid; i.e., they admit no non-trivial automorphisms. We later noted, essentially mimicking their technique, that the same is true of Δ1 ultrapowers (= “Nerode semirings”), a class of models of Π2 Arithmetic that...
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