Related papers: Equality and equivalence, intuitionistically
Let $T$ be a countable complete first-order theory with a definable, infinite, discrete linear order. We prove that $T$ has continuum-many countable models. The proof is purely first-order, but raises the question of Borel completeness of…
Brotherston and Simpson [citation] have formalized and investigated cyclic reasoning, reaching the important conclusion that it is at least as powerful as inductive reasoning (specifically, they showed that each inductive proof can be…
We develop first-order logic and some extensions for incomplete information scenarios and consider related complexity issues.
We develop new aspects of the the of numerosity theory; more exactly, we emphasize its relation with the ordinal numbers, cardinal numbers, hyperreal numbers and surreal numbers. In particular, we combine the notion of numerosity with the…
Intuitionistic logic extended with decidable propositional atoms combines classical properties in its propositional part and intuitionistic properties for derivable formulas not containing propositional symbols. Sequent calculus is used as…
We develop a bottom-up approach to truth-value semantics for classical logic of partial terms based on equality and apply it to prove the conservativity of the addition of partial description and partial selection functions, independently…
Preferential equality is an equivalence relation on fuzzy subsets of finite sets and is a generalization of classical equality of subsets. In this paper we introduce a tightened version of the preferential equality on fuzzy subsets and…
We look at equivalence relations on the set of models of a theory -- MERs, for short -- such that the class of equivalent pairs is itself an elementary class, in a language appropriate for pairs of models. We provide many examples of…
This paper presents and philosophically assesses three types of results on the observational equivalence of continuous-time measure-theoretic deterministic and indeterministic descriptions. The first results establish observational…
We introduce vectorial and topological continuities for functions defined on vector metric spaces and illustrate spaces of such functions. Also, we describe some fundamental classes of vector valued functions and extension theorems.
We study the conservativity of extensions by additional strict equalities of dependent type theories (and more general second-order generalized algebraic theories). The conservativity of Extensional Type Theory over Intensional Type Theory…
Quantifier-elimination or model-completeness of the affine part of some classical first order theories are proved.
This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is…
This note presents a unified theorem of the alternative that explicitly allows for any combination of equality, componentwise inequality, weak dominance, strict dominance, and nonnegativity relations. The theorem nests 60 special cases,…
We will investigate proof-theoretic and linguistic aspects of first-order linear logic. We will show that adding partial order constraints in such a way that each sequent defines a unique linear order on the antecedent formulas of a sequent…
I argue that, on a judicious reading of two existing criteria--one syntactic and the other semantic--dual theories can be taken to be empirically equivalent. The judicious reading is straightforward, but leads to the surprising conclusion…
We define a notion of "theory of (1,infty)-categories", and we prove that such a theory is unique up to equivalence.
The primary purpose of this article is to show that a certain natural set of axioms yields a completeness result for continuous first-order logic. In particular, we show that in continuous first-order logic a set of formulae is (completely)…
Many-valued logics in general, and fuzzy logics in particular, usually focus on a notion of consequence based on preservation of full truth, typical represented by the value 1 in the semantics given the real unit interval [0,1]. In a recent…
We establish some properties of \'etoiles and associated valuations over complex analytic spaces, showing that Abhyankar's inequality holds. We give some examples of pathological behavior of these valuations. We prove a regularization…