On the uniform one-dimensional fragment over ordered models
The uniform one-dimensional fragment U1 is a recently introduced extension of the two-variable fragment FO. The logic U1 enables the use of relation symbols of all arities and thereby extends the…
Heinrich Behmann's Contributions to Second-Order Quantifier Elimination from the View of Computational Logic
- Computer ScienceArXiv
An extensive documentation of the letters and manuscripts in Behmann's bequest that concern second-order quantifier elimination are given, including a commented register and English abstracts of the German sources with focus on technical material.
Novel threshold concepts in the mathematical sciences
The purpose of this research is to identify and examine some unusual, unexpected or novel threshold concepts in mathematics. This is ongoing work that contributes towards the development of a suite…
Historical Development of Modern Logic
- PhilosophyLogica Universalis
Modern Logic began in 1879, the year in which Gottlob Frege (1848–1925) published his Begriffsschrift. In less than ninety pages this booklet presented a number of discoveries that changed the face…
FIFTY YEARS OF THE SPECTRUM PROBLEM: SURVEY AND NEW RESULTS
In 1952, Heinrich Scholz published a question in the Journal of Symbolic Logic asking for a characterization of spectra, i.e., sets of natural numbers that are the cardinalities of finite models of…
Logical queries over views: Decidability and expressiveness
- Computer ScienceTOCL
The main result is the identification of a decidable class of first-order queries over unary conjunctive views that generalizes the decidability of the classical class offirst-order sentences over unARY relations known as the Löwenheim class.
Decidability vs. undecidability. Logico-philosophico-historical remarks
- PhilosophyAnn. UMCS Informatica
The aim of the paper is to present the decidability problems from a philosophical and historical perspective as well as to indicate basic mathematical and logical results concerning (un)decidability…
Model Theory ( Draft 20 Jul 00 )
In 1954 Alfred Tarski  announced that ‘a new branch of metamathematics’ had appeared under the name of the theory of models. The subject grew fast: the Omega Group bibliography of model theory…
How Peircean was the “‘Fregean’ revolution” in logic?
The historiography of logic conceives of a Fregean revolution in which modern mathematical logic (also called symbolic logic) has replaced Aristotelian logic. The preeminent expositors of this…
Fifty years of the spectrum problem: survey and new results
- MathematicsBull. Symb. Log.
The present disclosure involves a method of identifying animals involving the use of a universal identification scheme capable of identifying individual animals anywhere in the world such that data…