Characterizing classes defined without Equality
نویسنده
چکیده
In this paper we mainly deal with first-order languages without equality and introduce a weak form of equality predicate, the so-called Leibniz equality. This equality is characterized algebraically by means of a natural concept of congruence; in any structure, it turns out to be the maximum congruence of the structure. We show that first-order logic without equality has two distinct complete semantics (full semantics and reduced semantics) related by a reduction operator. The last and main part of the paper contains a series of Birkhoff-style theorems characterizing certain classes of structures defined without equality, not only full classes but also reduced ones.
منابع مشابه
Counterexamples of the 0-1 law for fragments of existential second-order logic: an overview
We propose an original use of techniques from random graph theory to find a Monadic Σ1 (Minimal Scott without equality) sentence without an asymptotic probability. Our result implies that the 0-1 law fails for the logics Σ1(FO ) and Σ1 (Minimal Gödel without equality). Therefore we complete the classification of first-order prefix classes with or without equality, according to the existence of ...
متن کاملCharacterizing sub-topical functions
In this paper, we first give a characterization of sub-topical functions with respect to their lower level sets and epigraph. Next, by using two different classes of elementary functions, we present a characterization of sub-topical functions with respect to their polar functions, and investigate the relation between polar functions and support sets of this class of functions. Finally, we obtai...
متن کاملA Silver-like Perfect Set Theorem with an Application to Borel Model Theory
Silvers’s perfect set theorem says that every Π1 equivalence relation over a polish space either has countably many equivalence classes or has a perfect set of inequivalent elements. We prove an analog where the equivalence relation is replaced by a Π1 dependence relation, and the perfect set of inequivalent elements is replaced by a perfect independent set. The dependence relation should satis...
متن کاملComplexity of Comparing the Domination Number to the Independent Domination, Connected Domination, and Paired Domination Numbers
The domination number γ(G), the independent domination number ι(G), the connected domination number γc(G), and the paired domination number γp(G) of a graph G (without isolated vertices, if necessary) are related by the simple inequalities γ(G) ≤ ι(G), γ(G) ≤ γc(G), and γ(G) ≤ γp(G). Very little is known about the graphs that satisfy one of these inequalities with equality. I.E. Zverovich and V...
متن کاملEquality of Streams is a Π2-Complete Problem
This paper gives a precise characterization for the complexity of the problem of proving equal two streams defined with a finite number of equations: Π2. Since the Π2 class includes properly both the recursively enumerable and the co-recursively enumerable classes, this result implies that one can find no mechanical procedure to say when two streams are equal, as well as no procedure to say whe...
متن کامل