Some interconnections between modern algebra and mathematical logic

Some Interconnections between Modern Algebra and Mathematical Logic«

Mathematical logic originated when mathematical methods were brought to bear on traditional questions of logic, especially the problem of what constitutes a valid proof. For the most part work in this field has remained close to foundational questions. Recent results, however, have indicated the possibility that the methods of mathematical logic may be of use in tackling specific problems in ot...

Universal Algebra and Mathematical Logic

In this paper, first-order logic is interpreted in the framework of universal algebra, using the clone theory developed in three previous papers [1] [2] and [3]. We first define the free clone T pL, Cq of terms of a first order language L over a set C of parameters in a standard way. The free right algebra FpL, Cq of formulas over the clone T pL, Cq of terms is then generated by atomic formulas...

On Some Interconnections between Combinatorial Optimization and Extremal Graph Theory

The uniting feature of combinatorial optimization and extremal graph theory is that in both areas one should find extrema of a function defined in most cases on a finite set. While in combinatorial optimization the point is in developing efficient algorithms and heuristics for solving specified types of problems, the extremal graph theory deals with finding bounds for various graph invariants u...

Symbioses between mathematical logic and computer science

The Mathematical Origins of 19 th Century Algebra of Logic ∗

Most 19th century scholars would have agreed to the opinion that philosophers are responsible for research on logic. On the other hand, the history of late 19th century logic clearly indicates a very dynamic development instigated not by philosophers, but by mathematicians. A central outcome of this development was the emergence of what has been called the “new logic”, “mathematical logic”, “sy...