Böhm's Theorem, Church's Delta, Numeral Systems, and Ershov Morphisms

EQ-logics with delta connective

In this paper we continue development of formal theory of a special class offuzzy logics, called EQ-logics. Unlike fuzzy logics being extensions of theMTL-logic in which the basic connective is implication, the basic connective inEQ-logics is equivalence. Therefore, a new algebra of truth values calledEQ-algebra was developed. This is a lower semilattice with top element endowed with two binary...

An Analysis of Böhm's Theorem

We present in this article a detailed analysis of Böhm’s theorem, explained completely constructively as an algorithmic development in the functional language ML.

Theory Morphisms in Church's Type Theory with Quotation and Evaluation

cttqe is a version of Church’s type theory with global quotation and evaluation operators that is engineered to reason about the interplay of syntax and semantics and to formalize syntax-based mathematical algorithms. cttuqe is a variant of cttqe that admits undefined expressions, partial functions, and multiple base types of individuals. It is better suited than cttqe as a logic for building n...

Böhm's theorem for Berarducci trees

From torsion theories to closure operators and factorization systems

Torsion theories are here extended to categories equipped with an ideal of 'null morphisms', or equivalently a full subcategory of 'null objects'. Instances of this extension include closure operators viewed as generalised torsion theories in a 'category of pairs', and factorization systems viewed as torsion theories in a category of morphisms. The first point has essentially been treated in [15].